Answer:
108
Step-by-step explanation:
"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:
score/18 = 24/4
Multiplying by 18, we get ...
score = 18(24/4) = 18(6) = 108
Nancy can expect a score of 108 on 18 holes.
Does this have any solutions -60x+32=32x-60
Answer:
x = 30
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION?
Jason is asked to draw a quadrilateral with the following specifications.
two adjacent angles are acute and congruent
opposite angles are supplementary
Which of the following statements about this quadrilateral is true?
A.
Exactly one quadrilateral exists with the given conditions, and it must be a parallelogram.
B.
More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.
C.
Exactly one quadrilateral exists with the given conditions, and it must be an isosceles trapezoid.
D.
More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.
Answer:
B. More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary. They are only congruent if the parallelogram is a rectangle. In this problem, adjacent angles are both congruent and acute. If this were a triangle, it would guarantee the triangle is isosceles.
The fact that opposite angles are supplementary guarantees that the fourth side of the figure is parallel to the base between the acute angles. That makes the figure an isosceles trapezoid. Unless specific angles and side lengths are specified, the description matches any isosceles trapezoid.
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 %
1/2(x + 1)²- 3
a. What is the "a" value?
b. What is the "h" value?
C. What is the "k" value?
Answer:
a = 1/2h = -1k = -3Step-by-step explanation:
We assume you want to compare your expression to the form ...
a(x -h)² +k
1/2(x +1)² +k
The multiplier outside parentheses is ...
a = 1/2
The horizontal offset inside parentheses is ...
-h = 1
h = -1
The vertical offset outside parentheses is ...
k = -3
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.
Learn more about the probability here:
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PLEASE I WILL GIVE BRAINLIEST!
Which of the following shows 7 + (x + 4y) rewritten using the Associative Property of Addition?
7 + x + 4y
7x + (4 + y)
(7 + x) + 4y
x + (7 + 4y)
Answer:
7 + x + 4y
(7 + x) + 4y
x + (7 + 4y)
Step-by-step explanation:
the sum of elements does not change, no matter the order.
What are the coordinates for this point?
Point D
Answer:
(-4, 0)
Step-by-step explanation:
We just need to identify where it is on both the x and y axis!
X Axis - Horizontal middle line.
Y Axis - Vertical middle line.
On the x-axis, you can see it is at -4, therefore we know our x is that.
On the y-axis, you can see it hasn't gone up or down from the vertex, showing us that it has neither gone up or down, so it is 0!
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
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
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
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.
g According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1630 children, 228 were found to be living with at least one grandparent. At a 5% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the p-value and the critical-value approaches.
Final answer:
At a 5% significance level, we can conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%. Both the p-value and critical-value approaches lead to the same conclusion.
Explanation:
To determine whether the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%, we will perform a hypothesis test using both the p-value and the critical-value approaches.
P-Value Approach:
The null hypothesis (H0) is that the proportion is equal to 11%, while the alternative hypothesis (Ha) is that the proportion is greater than 11%.We will calculate the sample proportion: p = 228/1630 = 0.1399.We will calculate the standard error of the proportion: SE = sqrt((0.11 * (1 - 0.11)) / 1630) = 0.0083.We will calculate the z-score: z = (0.1399 - 0.11) / 0.0083 = 3.5542.Using a significance level of 0.05, the critical value for a one-tailed test is approximately 1.645.Since the z-score of 3.5542 is greater than the critical value of 1.645, we reject the null hypothesis.The p-value associated with the test statistic is less than 0.0001, indicating strong evidence against the null hypothesis.Therefore, we can conclude at a 5% significance level that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.Critical-Value Approach:
Using a significance level of 0.05, the critical value for a one-tailed test is approximately 1.645.The test statistic, z = (0.1399 - 0.11) / 0.0083 = 3.5542.Since the test statistic is greater than the critical value, we reject the null hypothesis.Therefore, we can conclude at a 5% significance level that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.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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A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot.
Answer:
The height of tree house is 70.71 feet
Step-by-step explanation:
We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground
Refer the attached figure
Length of rope AC = Hypotenuse =100 feet
The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =[tex]\angle ACB = 45^{\circ}[/tex]
We are supposed to find the height of tree house i.e.AB = Perpendicular
So, Using trigonometric ratio
[tex]Sin \theta = \frac{perpendicular}{Hypotenuse}\\Sin 45= \frac{AB}{AC}\\\frac{1}{\sqrt{2}}=\frac{AB}{100}\\100 \times \frac{1}{\sqrt{2}}=AB\\70.71=AB[/tex]
Hence The height of tree house is 70.71 feet
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
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.
Stan ran 4 7/10 miles, which was 1 3/10 fewer miles than Matt ran. Four students wrote and solved equations to find m, the number of miles that Matt ran. Which student wrote and solved the equation correctly?
Answer: Miles ran by Matt = 6 miles
Step-by-step explanation: Miles ran by Stan = 4 7/10
i.e. 1 3/10 miles less than Matt.
∴ Miles ran by Matt = 4 7/10 + 1 3/10 = 60/10 = 6miles
∴ Miles ran by Matt = 6 miles
Answer:
The answer is A Mollys work
Step-by-step explanation:
I just did the work, and also it says "Fewer" which is subtraction but you need to change the subtraction to addition. And the answer is 6.
I hope this helps! <Dekomori Sanae(Engilish way to say it)/Sane Dekomori(Japanease way to say it)
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 the area of the shaded triangle?
72 mm2
096 mm2
120 mm2
0 150 mm
Answer:
96 on edg
Step-by-step explanation:
Answer:
96mm2 on Edge 2021
It maybe wrong if your not on edge depends on what the teachers think, lol.
What is the
numerator of the
fraction 3/5
Carol constructed a cube and marked each face with a number.
She marked the faces with the numbers 1, 2, 2, 3, 3, and 4. If she
rolls the cube twice, what is the probability that the sum of the
numbers will be exactly 7?
9514 1404 393
Answer:
1/9
Step-by-step explanation:
Carol can roll a total of 7 in two ways: 3 +4 or 4 + 3.
Two of the six faces are marked with 3, so the probability of rolling a 3 is 2/6 = 1/3. One of the six faces is marked with 4, so the probability of rolling a 4 is 1/6.
Then the probability of rolling a 3, then 4 is (1/3)(1/6) = 1/18. Similarly, the probability of rolling a 4, then 3 is (1/6)(1/3) = 1/18. These are presumed independent so the probability of one or the other of these outcomes is ...
1/18 +1/18 = 1/9
The probability that the sum is exactly 7 after two rolls is 1/9.
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.
More about the survey link is given below.
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Write an equation and solve this problem: Seventy is what percent of 50?
In which interval centered at the mean do 75% of the values drawn from this normal distribution lie? A) [33.7, 64.7] B) [37.7, 60.7] C) [40.7, 57.7] D) [43.7, 54.7]
Answer:
The Answer Is D
Step-by-step explanation:
I Juss Took It
evaluate 6ab when a = 1/2 and b = 7
Answer:21
Step-by-step explanation:
To evaluate 6ab with a = 1/2 and b = 7, you multiply 6 by 1/2 to get 3, and then multiply that by 7 to get 21, which is the final answer.
Explanation:To evaluate the expression 6ab when a = 1/2 and b = 7, you substitute the given values for a and b into the expression. This means you would multiply 6 by 1/2 and then by 7. The operation looks like this: 6 × (1/2) × 7.
First, simplify 6 × (1/2), which equals 3. Then multiply this result by 7, giving you 3 × 7 = 21.
Therefore, when a = 1/2 and b = 7, the expression 6ab evaluates to 21.
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:
The SAT is an exam that is used by many universities for admission. Suppose that the scores on the SAT mathematics exam have a normal distribution with mean 500 and standard deviation of 100. The statistics department identified students scoring in the top 4% of the SAT mathematics exam for recruitment. About what is the cutoff score for recruitment by the statistics department
Answer:
The cutoff score for recruitment by the statistics department is 675.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 500, \sigma = 100[/tex]
Cutoff score for the top 4%.
100-4 = 96th percentile, which is X when Z has a pvalue of 0.96. So X when Z = 1.75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.75 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = 1.75*100[/tex]
[tex]X = 675[/tex]
The cutoff score for recruitment by the statistics department is 675.
The SAT math scores have a mean of 500 and a standard deviation of 100, and using the z-score for the 96th percentile (approximately 1.75), we calculate the cutoff score.
The SAT mathematics exam scores are normally distributed with a mean (μ) of 500 and a standard deviation (σ) of 100. To find the cutoff score for the top 4%, we need to determine the z-score that corresponds to the 96th percentile (since 100% - 4% = 96%).
Using a z-table or calculator, the z-score for the 96th percentile is approximately 1.75. We can use the formula for the z-score:
Z = (X - μ) / σ
Solving for X (the cutoff score), we get:
1.75 = (X - 500) / 100
X - 500 = 1.75 × 100
X - 500 = 175
X = 675
Therefore, the cutoff score for recruitment by the statistics department is approximately 675. This means students need to score about 675 or higher on the SAT mathematics exam to be in the top 4%.
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.
A poll asked the following question: "If the military draft were reinstated, would you favor or oppose drafting women as well as men?" 45 percent of the 1000 people responding said that they would favor drafting women if the draft were reinstated. Using a 0.05 significance level, carry out a test to determine if there is convincing evidence that fewer than half of adult Americans would favor the drafting of women. (For z give the answer to two decimal places. For P give the answer to four decimal places.)
Answer:
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha < 0.50
z = -3.16
P value = P(Z<-3.16) = 0.0008
Decision we reject the null hypothesis and accept the alternative hypothesis. That is, there is convincing evidence that fewer than half of adult Americans would favor the drafting of women.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n=1000 represent the random sample taken
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha < 0.50
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 1000
po = Null hypothesized value = 0.50
p^ = Observed proportion = 0.45
Substituting the values we have
z = (0.45-0.50)/√{0.50(1-0.50)/1000}
z = -3.16
z = -3.16
To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.
P value = P(Z<-3.16) = 0.0008
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = -3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.