Answer:
[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
And the p value would be:
[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
Step-by-step explanation:
Information given
[tex]\bar X=1.8[/tex] represent the sample mean for the growth
[tex]s=0.5[/tex] represent the sample standard deviation
[tex]n=48[/tex] sample size
[tex]\mu_o =2[/tex] represent the value that we want to compare
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 2cm per week, the system of hypothesis are :
Null hypothesis:[tex]\mu \geq 2[/tex]
Alternative hypothesis:[tex]\mu < 2[/tex]
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
And the p value would be:
[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
You collect the following data on the air pressure of footballs ready for play. No data points are outside of the specification limits, so it appears the process is under control. However, you want to calculate the actual probability of a defect occurring in the future. Calculate this probability assuming the standard deviation does not change and that Tom Brady will not deflate the footballs right before the game.
Answer:
0.00086 or 0.086%
Step-by-step explanation:
The question is not complete, however, after searching online for the question, I was able to get the complete question.
Given that
USL = 14 ; CL = 13 ; LSL = 12
Probability of air pressure > 14 is equal to the Probability of air pressure <12 because the process is centered
Therefore, the probability of defect in future is equal to 2 × Probability of air pressure > 14
For us to discover the probability of pressure > 14, finding Z-value for X= 14 is important,
Mean Pressure (mu) =13
Std. Deviation (Sigma) = 0.3
Therefore;
Z = (X-mu)/sigma = (14-13)/0.3 = 3.33
From Standard normal distribution table for Z = 3.3, p = 0.99957
Hence,
the probability of pressure > 14 = 1 - 0.99957 = 0.00043
Finally, the probability of defect in future
= 2 × Probability of air pressure > 14
= 2 × 0.00043
= 0.00086
= 0.086 %
find the sum
thank you
Answer:
2x^3 -x
Step-by-step explanation:
x^3 -2x +2x^2 + x^3 -2x^2 +x
Combine like terms
x^3 + x^3 +2x^2 - 2x^2 -2x +x
2x^3 -x
Which shows the graph of the solution set of 6x + 4y < 12? On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (3, 1). Everything below and to the left of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (3, 1). Everything above and to the right of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the right of the line is shaded.
Answer:
(c) On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.
Step-by-step explanation:
You want a description of the graph of 6x +4y < 12.
InterceptsThe x-intercept will be the solution to ...
6x = 12 ⇒ x = 2, point (2, 0)
The y-intercept will be the solution to ...
4y = 12 ⇒ y = 3, point (0, 3)
ShadingThe form of the inequality ...
x < ( )
tells you the shading is left of the line, and the line is dashed. That is, solution set values of x are less than those on the line. The "or equal to" case is not included, so the line is not included in the solution set.
HELP PLEASE AND FAST
The city of Hamden received money for improvements of the town’s park. The park committee polled a random sample of 75 residents from the town. Of the 75 residents, 27 would like to see more trees planted in the park. From this information, what can be inferred? Most residents in the town would like to have more trees in the park. Exactly 36% of the residents in the town would like more trees in the park. About a third of the residents prefer a park improvement of more trees. Residents who use the park the most would like more trees planted.
Answer:
About a third of the residents prefer a park improvement of more trees.
Step-by-step explanation:
Less than 1/2 of the sample actually wanted more trees, so it isn't " Most residents in the town would like to have more trees in the park."
You (usually) can't get an exact answer with a sample, so it isn't ". Exactly 36% of the residents in the town would like more trees in the park."
You don't have enough data to say "Residents who use the park the most would like more trees planted."
Use the information in the table to find the constant of
proportionality and write the equation.
The constant of proportionality is
The equation that represents this proportional
relationship is
N
5
4
10
6
12.5
Answer:
2.5
and
y=2.5x
Step-by-step explanation:
Answer:
2.5
y=2.5x
Step-by-step explanation:
I hope you do good today I'm a little sad sorry I didn't do the joke of the day :(
What is the area of 6cm and 7cm in square centimeters
Answer:
42cm²
Step-by-step explanation:
b×h
6×7=42
area-To find the area of a rectangle multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
Answer:
42 sq cm
Step-by-step explanation:
6 x 7=42
Find the value of x.
Answer: 150
Step-by-step explanation: cause it has six side in total of 720 and subtract it and you have 150
Dot Products of Vectors
Quiz
Active
Find a b if a = 10i + 4j and b = 3i + 4%.
a. (30,16)
c. 46
b. -14
d. (13,8)
Answer:
choice c. 46
Step-by-step explanation:
Find a b if a = 10i + 4j and b = 3i + 4%
a = <10, 4>
b = <3, 4>
a*b = <10, 4> * <3, 4> = 10*3 + 4*4 = 30 + 16 = 46
Answer:
C. 46
Step-by-step explanation:
Answer now And I’ll give brainliest!
Micah wants to know the most common style of surfboard used at Breakers Point. He surveys surfers at Breakers Point between 8.00 AM and
12 PM Which of the following statements is true about Micah's survey? Select all that apply.
Answer: C
Step-by-step explanation:
The population for the survey is all people who surf at Breakers Point. And Micah will not get a representative sample. Then the correct options are C and D.
What is the survey?In order to gather information about a service, product, or process, a survey is described as an act of looking at a process or questioning a predetermined sample of people. Surveys used to gather data ask a specific set of people about their beliefs, actions, or knowledge.
Surveys are research techniques used to gather data from a designated group of respondents in order to learn more and acquire insights into a range of interesting topics. Depending on the methodology chosen and the objective of the study, they can be conducted in a variety of methods and serve a variety of objectives.
The population for the survey is all people who surf at Breakers Point. And Micah will not get a representative sample. Then the correct options are C and D.
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What is the perimeter of s triangle with side lengths of 5 cm, 8 cm, and 9 cm?
Answer:
22 cm
Step-by-step explanation:
The perimeter is the distance all the way around a shape. To find the perimeter, add up all the sides
The side lengths are 5, 8 and 9
5+8+9=22
So, the perimeter is 22 centimeters.
What is the base area of the cone?
°15 m2
°25 m2
°45 m2
°125 m2
V=75 m3
h=5m
Answer:
It is 45m2
Step-by-step explanation:
Just took did the question of the topic calculating the Base of Area of a Cone
Answer:
its 42 m^2
Step-by-step explanation: did it on edge
Briana has 1 red, 1 green, and 1 blue mechanical pencil in her
backpack. All of the pencils are the same size and shape. She
also has 1 red, 1 green, 1 blue, and 1 yellow eraser cap in the
backpack. All of the caps are the same size and shape. Briana
will randomly select 1 pencil and 1 cap. What is the probability
that she will select a pencil and a cap that are the same color?
Answer: one third of a chance
Step-by-step explanation:
The probability that she will select a pencil and a cap that is the same color is 1/4 option (C) 1/4 is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
Mechanical pencil: 1 red, 1 green, 1 blue
Erase cap: 1 red, 1 green, 1 blue, and 1 yellow.
P(both red) = (1/3)x(1/4) = 1/12
P(both green) = (1/3)x(1/4) = 1/12
P(both blue) = (1/3)x(1/4) = 1/12
P(same colour) = 1/12 + 1/12 + 1/12 = 3/12 = 1/4
Thus, the probability that she will select a pencil and a cap that is the same color is 1/4 option (C) 1/4 is correct.
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Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?
Answer:
Step-by-step explanation:
The question is incomplete. The missing part is shown in the comment box.
Mean = (697 + 759 + 1266 + 621 + 569 + 432)/6 = 724
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (697 - 724)^2 + (759 - 724)^2 + (1266 - 724)^2+ (621 - 724)^2 + (569 - 724)^2 + (432 - 724)^2 = 415616
Standard deviation = √415616/6 = 263.2
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 1000
For the alternative hypothesis,
µ > 1000
It is a right tailed test.
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t. The test statistic, t would be calculated with the formula below
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 724
µ = population mean = 1000
s = samples standard deviation = 263.2
t = (724 - 1000)/(263.2/√6) = - 2.57
We would determine the p value using the t test calculator. It becomes
p = 0.025
From the t distribution table, the critical value is 2.571
Since alpha, 0.05 > than the p value, 0.025, then we would reject the null hypothesis.
Therefore, at a 5% level of significance, the results do not suggest that all of the child booster seats meet the specified requirement.
The results suggests that the safety requirement for the hic measurement should be more than 1000 hic.
The day length in Juneau, Alaska, varies over time in a periodic way that can be modeled by a trigonometric function. Assume the length of the year (which is the period of change) is exactly 365365365 days. The longest day of the year is June 212121, and it's 1096.51096.51096, point, 5 minutes long. The shortest day of the year is half a year later, and it's 382.5382.5382, point, 5 minutes long. Note that June 212121 is 171171171 days after January 111. Find the formula of the trigonometric function that models the length LLL of the day ttt days after January 111. Define the function using radians.
Answer:
357cos(2π/365(t-171))+739.5
To model day length in Juneau, Alaska, a sine function with parameters calculated from the longest and shortest days is used. The function L(t) for the length of day in minutes, t days after January 1, is given by L(t) = 357 sin((2π/365)(t - 171)) + 739.5.
To model the length of day in Juneau, Alaska using a trigonometric function, we need to consider the longest and shortest day timings, the periodic nature of day length, and the fact that we're measuring time in minutes.
The function will have a sine function because the length of day varies sinusoidally, with the longest and shortest days being half a period apart.
The sine function to model day length L (in minutes) t days after January 1 will take the form:
L(t) = A sin(B(t - C)) + D
Where:
A is the amplitude, half the difference between the longest and shortest day lengths.
B is related to the period of the function, which is 2π divided by the number of days in a year.
C is the horizontal shift, which aligns the function with the longest day of the year.
D is the vertical shift, the average of the longest and shortest day lengths.
Let's calculate the amplitude (A), which is half the difference between the longest (1096.5 minutes) and shortest (382.5 minutes) day lengths:
A = (1096.5 - 382.5) / 2
A = 357
The period (B) can be calculated as:
B = 2π / 365
To find the horizontal shift (C), we use the fact that the longest day is on June 21, which is 171 days after January 1:
C = 171
The average day length (D), which is the vertical shift, is calculated:
D = (1096.5 + 382.5) / 2
D = 739.5
Finally, our function for day length L(t) is:
L(t) = 357 sin((2π/365)(t - 171)) + 739.5
For adults in the town of Bridgeport, systolic blood pressure is normally distributed with a mean of 134 mmHg and a standard deviation of 9 mmHg. What percentage of adults in the town have a systolic blood pressure less than 125 mmHg?
Answer: The percentage of adults that have a blodd pressure less than 125 mmHg is 15.87%
Step-by-step explanation:
In a normal distribution, we have that in the range:
(-∞, M) we have a 50%
(M, ∞) we have the other 50%.
(the infinite symbols are for notation, obviusly you can not have negative blood pressure)
where M is the mean.
If SD is the standard deviation, in the range
(M - SD, M) we have a 34.13%
Now, the values we have are: M = 134 mmHg, SD = 9mmHg
Then we can replace those values and get:
(M - SD, M) = (125mmHg, 134mmHg) = 34.13%
The range of blodd presure that is smaller than
Then, the range of blood pressure smaller than 125mmHg is the range between (-∞, 125mmHg)
We can calculate this proportion as:
(-∞. 134mmHg) - ( 125mmHg, 134mmHg) = 50% - 34.13% = 15.87%
The percentage of adults that have a blodd pressure less than 125 mmHg is 15.87%
The percentage of adults in the town of Bridgeport with a systolic blood pressure less than 125 mmHg is approximately 15.87%.
In this question, we are given that the systolic blood pressure of adults in the town of Bridgeport is normally distributed with a mean of 134 mmHg and a standard deviation of 9 mmHg.
We need to find the percentage of adults in the town who have a systolic blood pressure less than 125 mmHg.
To solve this, we can standardize the given value of 125 mmHg using the formula z = (x - μ) / σ, where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have z = (125 - 134) / 9 = -1. Here, we are interested in finding the area to the left of this z-score on the standard normal distribution curve.
Using a standard normal distribution table or a calculator, we can find that the percentage of adults in the town with a systolic blood pressure less than 125 mmHg is approximately 15.87%.
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If you roll a dice three times what is the probability of rolling an odd number each time
Answer:
3/6
Step-by-step explanation:
there are 6 sides: 3 odd and 3 even numbers
if you need to find the probability of rolling an odd number, take the number of odd possibilities and form a fraction with the number of total sides, 6.
so, 3/6 Or 1/2
Answer:
It would most likely be a 3 out of 6 chance per roll
Step-by-step explanation
With each roll there is a 50% percent chance of getting an odd number
The diameter of a beach ball is 10 inches. How many cubic inches of air can the beach ball hold? Use 3.14 for pi. Round to the nearest tenth of a cubic inch
Recall the formula Sphere V = 5
Answer:
The beach ball can hold 523.33 cubic inches of air
Step-by-step explanation:
Diameter of beach ball = 10 inches
Radius of beach ball =[tex]\frac{10}{2}= 5 inches[/tex]
We are supposed to find How many cubic inches of air can the beach ball hold
Volume of sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r is the radius
So, volume of sphere = [tex]\frac{4}{3} \times 3.14 \times 5^3=523.333 in^3[/tex]
Hence The beach ball can hold 523.33 cubic inches of air
Answer:
523.33
Step-by-step explanation:
125=m+110
i really need help plz
isolate m by subtracting 110 on both sides.
125=m+110
-110 -110
15=m
What is this expression in simplified form? (-7√3)(11√10)
Answer:
[tex]-77\sqrt{30}[/tex]
Step-by-step explanation:
[tex](-7\sqrt{3})(11\sqrt{10})=-77\sqrt{30}[/tex]
Hope this helps!
The simplified form of the expression is -77√33
Given the surd function (-7√3)(11√10)
Multiply the surd functions together. To do this, you multiply both the integers and the surd functions separately as shown:
(-7*11)(√3*√11)= (-77) √33= -77√33Hence the simplified form of the expression is -77√33
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Suppose an archaeologist discovers seven fossil skeletons from a previously unknown species of miniature horse. Reconstructions of the skeletons of these seven miniature horses show the shoulder heights (in centimeters) to be 45.3 47.1 44.2 46.8 46.5 45.5 47.6 For these sample data, the mean is x¯ = 46.14 and the sample standard deviation is s = 1.19. Let µ be the mean shoulder height (in centimeters) for this entire species of miniature horse, and assume that the population of shoulder heights is approximately normal. (a) Construct a 99% confidence interval for µ, the mean shoulder height of the entire population of such horses. (b) Someone claims that the mean shoulder heights of these horses is about 48 cm or higher. Based on the confidence interval, is it reasonable to believe this? (c) If the sample size were n = 10, would the confidence interval be narrower or wider?
Answer:
a) [tex]46.14-3.707\frac{1.19}{\sqrt{7}}=44.47[/tex]
[tex]46.14+3.707\frac{1.19}{\sqrt{7}}=47.81[/tex]
b) For this case the upper limit for the confidence interval is lower than 48 so then at 1% of significance we can't conclude that the claim given is true.
c) [tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
If we reduce the sample size from 30 to 10 we will have an interval wider since the margin of error would be larger
Step-by-step explanation:
Data given
[tex]\bar X=46.14[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s=1.19 represent the sample standard deviation
n=7 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=7-1=6[/tex]
The Confidence level is 0.99 or 99%, the significance would be [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value for this case is [tex]t_{\alpha/2}=3.707[/tex]
Replacing we got:
[tex]46.14-3.707\frac{1.19}{\sqrt{7}}=44.47[/tex]
[tex]46.14+3.707\frac{1.19}{\sqrt{7}}=47.81[/tex]
Part b
For this case the upper limit for the confidence interval is lower than 48 so then at 1% of significance we can't conclude that the claim given is true.
Part c
For this case we need to take in count that the margin of error is given by:
[tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
If we reduce the sample size from 30 to 10 we will have an interval wider since the margin of error would be larger
David is designing a t-shirt for the choir pop show. The cost of printing is $400 plus $7.50 per shirt. What is the average total cost per shirt if 85 shirts are sold? Round to the nearest cent.
Answer:
average cost ≈ $12.21 (nearest cent)
Step-by-step explanation:
The cost of printing the shirt is $400 plus $7.50 per shirt. The cost for producing the shirt requires a flat rate of $ 400 plus an additional $7.50 for each shirt.
Let
x = number of shirt
total cost = 400 + 7.50(x)
The number of shirt sold = 85
The average cost per shirt can be calculated as follows when he sold 85 shirts.
Average cost = total cost/number of shirt
total cost = 400 + 7.50(x)
total cost = 400 + 7.50(85)
total cost = 400 + 637.50
total cost = $1037.5
number of shirt = 85
average cost per shirt = 1037.5/85
average cost = 12.205882353
average cost ≈ $12.21 (nearest cent)
Which of these shows a right angle
Answer:
the 1st one
Step-by-step explanation:
A basketball player participates in a one-and-one free throw situation. The player has a 80% free throw average. What is the probability the player gets 2 points?
Answer:
80%
Step-by-step explanation:
Bob ordered 17 yards of lumber to build a treehouse how many inches of lumber did he order
Answer:
six hunddered n twelve
Step-by-step explanation:
The data in the table represents the value of a savings
account at the end of each year for 6 years. The
relationship between the increasing years and the
increasing value of the account is exponential.
There is [ ]
rate of change in an
exponential relationship
After each year, the value of the account is[. ]times as
large as the previous year
First missing either a constant additive, or a constant multiplicative, or no constant
Second missing word either 0.5 or 1.05 or 1.5 or 2
Answer:
The answer is constant multiplicative and it is 1.05 times larger.
There is constant rate of change in an exponential relationship.
The value of the account is 1.05 times.
In the given statement, it states that there is a [ ] rate of change in an exponential relationship. The missing word in this case would be "constant."
In an exponential relationship, the rate of change between consecutive terms is constant.
Now, after each year, the value of the account is [. ] times as large as the previous year. The missing value in this case would be "1.05."
This indicates that the value of the account increases by a factor of 1.05 each year, which corresponds to a 5% annual growth rate.
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For what values do maximum r-values occur on the graph the polar equation
r=-3 + 4 cos theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.
Answer:
We have the function:
r = -3 + 4*cos(θ)
And we want to find the value of θ where we have the maximum value of r.
For this, we can see that the cosine function has a positive coeficient, so when the cosine function has a maximum, also does the value of r.
We know that the meaximum value of the cosine is 1, and it happens when:
θ = 2n*pi, for any integer value of n.
Then the answer is θ = 2n*pi, in this point we have:
r = -3 + 4*cos (2n*pi) = -3 + 4 = 1
The maximum value of r is 7
(while you may have a biger, in magnitude, value for r if you select the negative solutions for the cosine, you need to remember that the radius must be always a positive number)
Answer:
the correct answer is d.pi
Step-by-step explanation:
I just took the quiz
which is the equation of a circle with diameter AB with A(5, 4) and B(- 1, - 4)
The equation of the circle with diameter AB and endpoints A(5, 4) and B(-1, -4) is (x - 2)² + y² = 25.
We have,
To find the equation of a circle given the diameter endpoints, use the midpoint formula and the distance formula.
Given the diameter endpoints:
A(5, 4) and B(-1, -4)
Step 1:
Find the midpoint of the diameter.
The midpoint formula is given by:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Let's calculate the midpoint using the coordinates of A and B:
Midpoint = ((5 + (-1)) / 2, (4 + (-4)) / 2)
Midpoint = (4 / 2, 0 / 2)
Midpoint = (2, 0)
Step 2:
Find the radius of the circle.
The radius is the distance between the midpoint and one of the endpoints, A or B.
The distance between the midpoint and point A:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Distance = √((5 - 2)² + (4 - 0)²)
Distance = √(3² + 4²)
Distance = √(9 + 16)
Distance = √25
Distance = 5
The radius of the circle is 5.
Step 3:
Write the equation of the circle.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
Using the midpoint as the center (h, k) and the radius we calculated:
(x - 2)² + (y - 0)² = 5²
(x - 2)² + y² = 25
Therefore,
The equation of the circle with diameter AB and endpoints A(5, 4) and B(-1, -4) is (x - 2)² + y² = 25.
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g Assume that the distribution of time spent on leisure activities by adults living in household with no young children is normally distributed with a mean of 4.5 hours per day and a standard deviation of 1.3 hours per day. Find the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day. Round your answer to four decimal places. (make sure to put a 0 in front of the decimal ie 0.1 vs .1)
Answer:
"The probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day" is about 0.8749.
Step-by-step explanation:
We have here a random variable that is normally distributed, namely, the time spent on leisure activities by adults living in a household with no young children.
The normal distribution is determined by two parameters: the population mean, [tex] \\ \mu[/tex], and the population standard deviation, [tex] \\ \sigma[/tex]. In this case, the variable follows a normal distribution with parameters [tex] \\ \mu = 4.5[/tex] hours per day and [tex] \\ \sigma = 1.3[/tex] hours per day.
We can solve this question following the next strategy:
Use the cumulative standard normal distribution to find the probability.Find the z-score for the raw score given in the question, that is, x = 6 hours per day.With the z-score at hand, we can find this probability using a table with the values for the cumulative standard normal distribution. This table is called the standard normal table, and it is available on the Internet or in any Statistics books. Of course, we can also find these probabilities using statistics software or spreadsheets.We use the standard normal distribution because we can "transform" any raw score into standardized values, which represent distances from the population mean in standard deviations units, where a positive value indicates that the value is above the mean and a negative value that the value is below it. A standard normal distribution has [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex].
The formula for the z-scores is as follows
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Solving the question
Using all the previous information and using formula [1], we have
x = 6 hours per day (the raw score).
[tex] \\ \mu = 4.5[/tex] hours per day.
[tex] \\ \sigma = 1.3[/tex] hours per day.
Then (without using units)
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{6 - 4.5}{1.3}[/tex]
[tex] \\ z = \frac{1.5}{1.3}[/tex]
[tex] \\ z = 1.15384 \approx 1.15[/tex]
We round the value of z to two decimals since most standard normal tables only have two decimals for z.
We can observe that z = 1.15, and it tells us that the value is 1.15 standard deviations units above the mean.
With this value for z, we can consult the cumulative standard normal table, and for this z = 1.15, we have a cumulative probability of 0.8749. That is, this table gives us P(z<1.15).
We can describe the procedure of finding this probability in the next way: At the left of the table, we have z = 1.1; we can follow the first line on the table until we find 0.05. With these two values, we can determine the probability obtained above, P(z<1.15) = 0.8749.
Notice that the probability for the z-score, P(z<1.15), of the raw score, P(x<6) are practically the same, [tex] \\ P(z<1.15) \approx P(x<6)[/tex]. For an exact probability, we have to use a z-score = 1.15384 (without rounding), that is, [tex] \\ P(z<1.15384) = P(x<6) = 0.8757[/tex]. However, the probability is approximated since we have to round z = 1.15384 to z = 1.15 because of the use of the table.
Therefore, "the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day" is about 0.8749.
We can see this result in the graphs below. First, for P(x<6) in [tex] \\ N(4.5, 1.3)[/tex] (red area), and second, using the standard normal distribution ([tex] \\ N(0, 1)[/tex]), for P(z<1.15), which corresponds with the blue shaded area.
Final answer:
The question seeks to find the probability that an adult spends less than 6 hours per day on leisure activities, using the given mean and standard deviation for a normal distribution. The z-score is calculated and then used to determine the probability using the cumulative normal distribution function.
Explanation:
The student's question asks to find the probability that a randomly selected adult from a certain population spends less than 6 hours per day on leisure activities, given that the distribution of time spent is normally distributed with a mean of 4.5 hours and a standard deviation of 1.3 hours.
To solve this, you can use the z-score formula:
z = (X - μ) / σ
where X is the value of interest (6 hours), μ is the mean (4.5 hours), and σ is the standard deviation (1.3 hours).
Using this, we calculate:
z = (6 - 4.5) / 1.3
= 1.15 / 1.3
= 0.8846
Now, we look up this z-score in a standard normal distribution table or use a calculator with the normal distribution function to find the corresponding probability.
Assuming normal CDF is the function for cumulative normal distribution:
probability = CDF(-∞, 0.8846, 0, 1)
This will give us the probability that the adult spends less than 6 hours per day on leisure activities. Remember, the cumulative distribution function gives the area to the left of the z-score, which corresponds to the probability of obtaining a value less than the one of interest.
9. A small airplane is 60 miles from the airport and is going down for landing with some angle of depression. However its navigation device malfunctions and incorrectly shows the distance to be 65 miles. The dispatcher noticed this mistake and figured out that if airplane continues on its current course, it will end up 16 miles from airport. By how many degrees should dispatcher adjust the airplane heading
Answer:
13.98 degrees
Step-by-step explanation:
Let the airplane be at point A, the airport at point B and the point of overshoot, point C.
If the plane is on path AC and the pilot wants to adjust to the path AB, the angle by which the pilot will adjust the airplane heading is the angle between AB and AC which is A.
Using Cosine Rule
[tex]Cos A=\dfrac{b^2+c^2-a^2}{2bc} \\Cos A=\dfrac{65^2+60^2-16^2}{2(65)(60)} \\Cos A=0.9704\\A=arcCos (0.9704)\\\angle A=13.98^\circ[/tex]
The pilot should adjust the plane's heading by 13.98 degrees.
There are four entrances to the Government Center Building in downtown Philadelphia. The building maintenance supervisor would like to know if the entrances are equally utilized. To investigate, 401 people were observed entering the building. The number using each entrance is reported below. At the 0.01 significance level, is there a difference in the use of the four entrances? Entrance Frequency Main Street 81
Answer:
Yes. We have evidence to support the claim that there is a difference in the use of the four entrances.
Step-by-step explanation:
The question is incomplete:
Entrance Frequency
Main Street 81
Broad Street 129
Cherry Street 72
Walnut Street 119
Total: 401
The building maintenance supervisor wants to know if the entrances are equally utilized.
This problem can be solved using the Chi-square goodess of fit test.
The expected value for each door is
[tex]E=401/4=100.25[/tex]
The degrees of freedom are equal to the number of categories (4 doors) minus one:
[tex]df=n-1=4-1=3[/tex]
Then, the value of the chi-square statistic can be calculated as:
[tex]\chi^2=\sum \dfrac{(O_i-E)^2}{E}\\\\\\\chi^2=\dfrac{(81-100.25)^2}{100.25}+\dfrac{(129-100.25)^2}{100.25}+\dfrac{(72-100.25)^2}{100.25}+\dfrac{(119-100.25)^2}{100.25}\\\\\\\chi^2=\dfrac{370.5625+826.5625+798.0625+351.5625}{100.25}=\dfrac{2346.75}{100.25}=23.41[/tex]
The P-value for this test statistic χ^2=23.41 and df=3 is:
[tex]P-value=P(\chi^2_3>23.41)=0.00003[/tex]
This P-value is much smaller than the significance level (0.01), so the effect is significant.
We have evidence to support the claim that there is a difference in the use of the four entrances.