Answer:
The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.
Step-by-step explanation:
The random variable X is defined as the time a new thunderstorm begins to produce rain.
The random variable X is uniformly distributed throughout the day, i.e. between the 24 hours a day or 1440 minutes.
[tex]X\sim Uniform\ [0, 1440][/tex]
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
It is provided that it will rain at some point both of the next two days.
Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM as follows:
9:10 AM = (9 × 60) + 10 = 550 minutes.
3:30 PM = 15:30 = (15 × 60) + 30 = 930 minutes.
Compute the value of P (550 < X < 930) as follows:
[tex]P(550<X<930)=\int\limits^{930}_{550}{\frac{1}{1440-0}}\, dx\\\\=\frac{1}{1440}\times \int\limits^{930}_{550}{1}\, dx\\\\=\frac{1}{1440}\times [x]^{930}_{550}\\\\=\frac{930-550}{1440}\\\\=0.2639[/tex]
The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM is 0.2639.
Then the complement of this event is:
The probability that the first drop of rain will not be felt between 9:10 AM and 3:30 PM is:
P (Not between 9:10 AM and 3:30 PM) = 1 - 0.2639 = 0.7361
Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days as follows:
P (At least 1) = 1 - P (Less than 1)
= 1 - P (None)
= 1 - P (Not between 9:10 AM and 3:30 PM)
= 1 - 0.7361
= 0.2639
Thus, the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.
PLEASEE HELP WILL mark BRAINLIEST
Answer:
The volume of the sphere is 972π mm³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 9mm
π = pi
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * π * (9mm)³
V = π * ⁴⁄₃ *729mm³
V = π * 972mm³
V = 972π mm³
The volume of the sphere is 972π mm³
14. Find the height of a cylinder if the surface area is 408.41 square inches and the radius is 5
inches.
Final answer:
To find the height of a cylinder with a given surface area and radius, use the formula for the surface area of a cylinder. In this case, the height is approximately 4 inches.
Explanation:
Surface Area of a Cylinder Formula: S = 2πrh + 2πr²
Given: surface area = 408.41 sq in, radius = 5 in
Plug in the values: 408.41 = 2π(5)h + 2π(5)²
Solve for height: h = (408.41 - 50π) / 10π ≈ 4 in
Therefore, the height of the cylinder is approximately 4 inches.
What is the best example of a negative correlation?
Question 1 options:
Volleyball practices in a week and the amount of free time that week.
The amount of time spent jogging and calories burned.
Students in a classroom and number of chairs in the classroom.
The altitude of a plane and the number of passengers on board.
Answer:
gergverkngvneropgeronhnernih[eh[neirvhier,hn[eriin[hnerohper'her
Step-by-step explanation:
Answer:
Common Examples of Negative Correlation. A student who has many absences has a decrease in grades. As weather gets colder, air conditioning costs decrease. If a train increases speed, the length of time to get to the final point decreases.
The heights of all adult males in Croatia are approximately normally distributed with a mean of 180 cm and a standard deviation of 7 cm. The heights of all adult females in Croatia are approximately normally distributed with a mean of 158 cm and a standard deviation of 9 cm. If independent random samples of 10 adult males and 10 adult females are taken, what is the probability that the difference in sample means (males – females) is greater than 20 cm?
Answer:
Step-by-step explanation:
.7104
The probability that the difference in sample means (males – females) is greater than 20 cm is; 0.7088
How to find difference between two means?The formula for z-score of difference between two means is;
z = (x₁' - x₂' - Δ)/√[(√σ₁²/n₁) + (σ₂²/n₂)]
We are given;
Sample mean 1; x₁' = 180 cm
Sample mean 2; x₂' = 158 cm
Standard deviation 1; σ₁ = 7 cm
Standard Deviation 2; σ₂ = 9 cm
hypothesized difference; Δ = 20 cm
Sample size; n₁ = n₂ = 10
Thus;
z = (180 - 158 - 20)/√[(7²/10) + (9²/10)]
z = 0.55
From online z-score table, we have;
p = 0.71
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3
0 +
x+1
2
≤ −
3x+1
4
Answer:
solve for x
x ≤ − 7
The distance travelled in (m) by a ball dropped from a height are 128/9,32/3,8,6,...
How much distance will it travel before coming to rest
Answer: it will trave 56.89 meters before coming to rest.
Step-by-step explanation:
This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as
S = a/(1 - r)
where
S = sum of the distance travelled by the ball
a = initial distance or height of the ball
r = common ratio
From the information given,
a = 128/9
r = (32/3)/(128/9) = 0.75
Therefore,
S = (128/9)/(1 - 0.75) = 56.89 meters
The distance travelled is an illustration of the sum to infinity of a geometric sequence.
The ball will a travel 56.89 meters before coming to rest
The sequence is given as:
[tex]\mathbf{128/9, 32/3, 8, 6....}[/tex]
From the sequence above, we have:
[tex]\mathbf{a = 128/9}[/tex] --- the first term
[tex]\mathbf{r = 6/8 = 3/4}[/tex] -- the common ratio
The sum to infinity of a geometric progression is:
[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]
So, we have:
[tex]\mathbf{S_{\infty} = \frac{128/9}{1-3/4}}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128/9}{1/4}}[/tex]
Divide
[tex]\mathbf{S_{\infty} = \frac{128}{9} \times 4}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128\times 4}{9} }[/tex]
[tex]\mathbf{S_{\infty} = \frac{512}{9} }[/tex]
[tex]\mathbf{S_{\infty} = 56.89}[/tex]
Hence, the ball will a travel 56.89 meters before coming to rest
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Marsha wants to determine the vertex of the quadratics vertex of the quadratics functions f(x)=x^2-x+2
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Suppose we have a quadratic equation in the following format:
[tex]y = f(x) = ax^{2} + bx + c[/tex]
The vertex of the function is the point [tex](x_{v}, f(x_{v})[/tex], in which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this problem:
[tex]f(x) = x^{2} - x + 2[/tex]
This means that [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]x_{v} = -\frac{-1}{2} = \frac{1}{2}[/tex]
[tex]f(x_{v}) = f(\frac{1}{2}) = (\frac{1}{2})^{2} - \frac{1}{2} + 2 = \frac{1}{4} - \frac{1}{2} + 2 = \frac{1 - 2 + 8}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
A polling organization had taken a survey of a sample of 200 people for one of their clients, in order to estimate a population percentage. Now the client would like them to reduce the margin of error by 50% (that is, the new margin of error should be half the original margin of error), while keeping the same level of confidence. To do this, how many people should they now survey
Answer:
They now should survey 800 people.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Same level of confidence, so same z
Same proportion, so same [tex]\pi[/tex]
We have to change n
We want to reduce the margin of error by half.
M is inverse proportion to the square root of n. That is, as n increases, M decreases.
We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4
The first survey had a sample of 200 people
Increasing by a factor of 4.
200*4 = 800
They now should survey 800 people.
Paul wants to write equations in the form y=mx+b for the lines passing through point D that are parallel and perpendicular to line h. First he finds the slopes of these two lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinate of D into the equations and solve for b for each equation
Step-by-step explanation:
The equation for a line is y = mx+b
where m is the slope and b is the y intercept
We know m
We have a point (x,y)
We can substitute into the equation and solve for b
Answer:
First option
Step-by-step explanation:
In y = mx + b, m is the slope and b is the y-intercept
Plug in m, and coordinates of D and solve for b
Find the length of the arc. Round to the nearest tenth.
Answer:28.8 m
Step-by-step explanation:
length of arc=theta/360 x 2 x π x radius
Length of arc=150/360 x 2 x3.14x11
length of arc=(150x2x3.14x11) ➗ 360
Length of arc =10362 ➗ 360
Length of arc =28.8
Kai ate an ice cream cone at the park last Thursday. The height of the cone was 7
centimeters. The diameter of the base is 4 centimeters. What would be the Volume
of the cone?
Choose a answer
23.2
29.3
40.4
500000000000
Answer:
29.3
Step-by-step explanation:
For Ice-cream Cone
height (h) = 7 cm
diameter (d) = 4 cm
radius (r) = diameter/2 = 4/2 cm
radius (r) = 2 cm
Volume Of A Cone
= π * r^2 * h/3
= 22/7 * 2 * 2 * 7/3
= 22 * 4 * 1/3 cm
= 88/3 cm
= 29.3 cm^3
Thus, the Volume of the cone would be 29.3 cm^3
Gary used 8 gallons of gas to travel 176 miles. How many miles can Gary travel on 1 gallon of gas
Answer: Gary can travel 22 miles on 1 gallon gas.
Step-by-step explanation:
176/8 = 22
suppose the null hypothesis is rejected. state the conclusion based on the results of the test. six years%E2%80%8B ago, 11.4% of registered births were to teenage mothers. a sociologist believes that the percentage has increased since then. which of the following is the correct%E2%80%8B conclusion? a. there is sufficient evidence to conclude that the percentage of teenage mothers has increased. b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. c. there is not sufficient evidence to conclude that the percentage of teenage mothers has increased. d. there is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Answer: the correct option is B
Step-by-step explanation:
The question is incorrect. The correct one is:
Suppose the null hypothesis is rejected. State the conclusion based on the results of the test. Six years ago, 11.4% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. which of the following is the correct conclusion? a. there is sufficient evidence to conclude that the percentage of teenage mothers has increased. b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. c. there is not sufficient evidence to conclude that the percentage of teenage mothers has increased. d. there is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Solution:
This is a test of two population proportions. We would set up the hypothesis. The given proportion is 11.4/100 = 0.114
For the null hypothesis,
p = 0.114
For the alternative hypothesis,
p < 0.114
Since the null hypothesis is rejected, it means that there was sufficient evidence to reject it and the alternative hypothesis is accepted. the correct conclusion would be
b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Final answer:
When the null hypothesis is rejected, it indicates there is enough evidence to support the alternative hypothesis. In this case, the result would suggest an increase in the percentage of teenage mothers from six years ago.
Explanation:
If the null hypothesis is rejected, the correct conclusion would be that there is sufficient evidence to support the alternative hypothesis. In this scenario, the sociologist believes that the percentage of teenage mothers has increased since six years ago. Therefore, if we reject the null hypothesis, our conclusion would be option (a) - there is sufficient evidence to conclude that the percentage of teenage mothers has increased.
x 2 + 13x + 40 = 0
solving quadratic
Answer: x=-5 or x=-8
Step-by-step explanation:
x^2+13x+40=0
x^2 + 8x + 5x +40=0
x(x+8)+5(x+8)=0
(x+5)(x+8)=0
x+5=0 or x+8=0
x=-5 or x=-8
What is the measure of arc AD?
Angle ABD measures (4x + 10). Angle ACD measures
(5x - 2)
GO
Answer:
116°
Step-by-step explanation:
Given that :
∠ ABD measures (4x + 10)
∠ ACD measures (5x - 2)
Then
∠ABD = ∠ACD ( rule : angle by same chord AD )
∠ABD = (4x + 10)°
∠ACD = (5x - 2)°
so we can as well say that :
(4x + 10)° = (5x - 2)°
4x - x = -10 -2
- x = - 12
x = 12
∠ABD = (4x + 10)°
= ( 4 × 12 + 10)°
= 58°
∠ACD = (5x - 2)°
= ( 5 * 12 - 2)°
= 58°
∠AOD = 2∠ABD = 2∠ACD ( since angle by arc AD at center is twice the angle by same arc AC in other arc segment)
∠AOD = 2 × 58°
∠AOD = 116°
Measure of arc AD = 116°
The mean number of sick days per employee taken last year by all employees of a large city was 10.6 days. A city administrator is investigating whether the mean number of sick days this year is different from the mean number of sick days last year. The administrator takes a random sample of 40 employees and finds the mean of the sample to be 12.9. A hypothesis test will be conducted as part of the investigation.
Which of the following is the correct set of hypotheses?
A. H0:μ=10.6Ha:μ>10.6 AB. H0:μ=10.6Ha:μ≠10.6 BC. H0:μ=10.6Ha:μ<10.6 CD. H0:μ=12.9Ha:μ≠12.9 DE. H0:μ=12.9Ha:μ<12.9 E
Answer:
H0:μ=10.6
Ha:μ≠10.6
Step-by-step explanation:
you do not find out about the 12.9 until after stating the hypothesis.
The correct hypothesis set for testing whether the mean number of sick days has changed is H0: μ = 10.6 against Ha: μ ≠ 10.6, which represents a two-tailed test.
Explanation:The correct set of hypotheses for the city administrator to test whether the mean number of sick days this year is
different from last year would be:
H0: μ = 10.6Ha: μ ≠ 10.6This is because the administrator is investigating if there is a change in either direction (increase or decrease), which is
considered a two-tailed test.
The null hypothesis (H0) always states that there is no difference or no effect, while the alternative hypothesis (Ha)
suggests that there is a difference from the norm, in that the mean is not equal to 10.6 days.
Based on the information given, the correct answer would be:
B. H0: μ = 10.6
Ha: μ ≠ 10.6
solve for x x/25 > 5
Answer:
x > 125
Step-by-step explanation:
x/25 > 5
Multiply both sides by 25
x/25 × 25 > 5 × 25
x > 125
There were 47 ducks swimming in a pond. A dog jumped into the pond and scared 29 of the ducks away. After
the dog got out, 5 groups of 3 ducks returned to the pond.
Answer:
Step-by-step explanation:
Originally, there were 47 ducks. After the dog jumped in, there were 29. This means there were 18 ducks.
47 - 29 = 18
After the dog got out 5 groups of 3 ducks came. This means that 15 ducks came back.
5 × 3 = 15
To find the total amount of ducks, add the ducks together.
18 + 15 = 33
To find the number of ducks remaining in the pond, subtract the 29 ducks scared away from the initial 47, then add the 15 ducks that returned in 5 groups of 3, resulting in 33 ducks now present in the pond.
Explanation:The student has asked a question related to a basic arithmetic problem involving ducks in a pond. Initially, there were 47 ducks in the pond. A dog scares 29 ducks away. After the dog leaves, 5 groups of 3 ducks each return to the pond. To solve this, we perform two main steps:
Subtract the number of ducks that were scared away by the dog: 47 - 29 = 18 ducks remaining.Calculate the total number of ducks returning: 5 groups * 3 ducks/group = 15 ducks returning.Add the ducks that returned to the remaining ducks in the pond: 18 + 15 = 33 ducks are now in the pond after the disturbance and return.
What is the measure of c?
45°
56°
60°
66°
Answer:
56
Step-by-step explanation:
Just took the quiz
Hope this helps!
Determine the measures of the unknown angles in the figure.
m∠APD =
m∠CPE =
m∠BPD =
Answer:
Step-by-step explanation:
Lines A B, C D, and D P intersect at point P. Angle A P C is 65 degrees, Angle C P E is blank, angle E P B is 90 degrees, and angle B P D is blank.
Determine the measures of the unknown angles in the figure.
m∠APD =
✔ 115°
m∠CPE =
✔ 25°
m∠BPD =
✔ 65°
The measure of unknown angles
m∠APD = 115
m∠CPE = 25
m∠BPD = 65
What is Linear Pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. They are also referred to as additional angles. Angles that share a vertex are said to be neighbouring. Hence, the linear angles have a common vertex in this instance as well.
Using Linear Pair
<APC + <CPE + <EPB = 180
65 + <CPE + 90 = 180
<CPE = 180 - 155
<CPE = 25
So, <APD = 90 + 25 = 115 degree
<CPE = 25 degree
<BPD = <APC = 65 degree (Vertically opposite angle)
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Suppose we know that the birth weight of babies is normally distributed with mean 3500g
and standard deviation 500g.
(1) What is the probability that a baby is born that weighs less than 3100g?
a. What are the parameters?
b. Construct the normal distribution density curve, then shade your seeking area.
c. Find the Z-score, and construct the standard normal distribution density curve,
then shade your seeking area.
d. Find the probability.
Answer:
a) [tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
b) For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
c) For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
d) We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
Step-by-step explanation:
For this problem we define the random variable of interest X defined as "the birth weigth of babies" and the distribution for this variable is normal
Part a
The parameters are given:
[tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
Part b
For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
Part c
For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
Part d
We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
What’s the distance between point A (32,15) and point B (32,29
Answer:
14 units
Step-by-step explanation:
Both points lie on the vertical line x=32, so the distance between them is the difference of their y-coordinates:
29 -15 = 14 . . . . units
The two points are 14 units apart.
Answer:
[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]
So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14
Step-by-step explanation:
When we have a two points on a dimensional space A and B we can find the distance between the two points with the following formula:
[tex] d= \sqrt{(x_A -x_B)^2 +(y_A -y_B)^2}[/tex]
Where (x_A,y_A) represent the coordinates for the point A and (x_B,y_B) represent the coordinates for the point B. And we know that the coordinates are :
A= (32,15) and B= (32,29)
And replacing in the formula for the distance we got:
[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]
So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14
In 2001 polls indicated that 74% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2001? We test the hypothesis that the percentage supporting mandatory testing is less than 74% this year. The P-value is 0.015. Which of the following interpretation of this P-value is valid? Group of answer choices The probability that Americans have changed their opinion on this issue since 2001 is 0.015. If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion. There is a 1.5% chance that the null hypothesis is true.
Answer:
The correct option is option 2.
Step-by-step explanation:
In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.
The hypothesis can be defined as follows:
H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.
Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.
It is provided that the p-value of the test is,
p-value = 0.015
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.
Thus, the correct option is option 2.
The Internet is affecting us all in many different ways, so there are many reasons for estimating the proportion of adults who use it. Assume that a manager for E-‐Bay wants to determine the current percentage of U.S. adults who now use the Internet. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points? a. b. In 2006, 73% of adults used the Internet. No known possible value of the proportion.
Answer:
a) At least 842 adults must be surveyed.
b) At least 1068 adults must be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
a) 73% of adults used the Internet.
At least n adults must be surveyed.
n is found when [tex]M = 0.03, \pi = 0.73[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.73*0.27}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.73*0.27}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.73*0.27}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.73*0.27}}{0.03})^{2}[/tex]
[tex]n = 841.3[/tex]
Rounding up
At least 842 adults must be surveyed.
b. No known possible value of the proportion.
Same as above, the difference as the since we do not know the value of the proportion, we use [tex]\pi = 0.5[/tex], which is when the largest sample size is going to be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.03})^{2}[/tex]
[tex]n = 1067.11[/tex]
Rounding up
At least 1068 adults must be surveyed.
To be 95% confident that the sample percentage of U.S. adults who use the Internet is in error by no more than 3 percentage points, a total of 1068 adults must be surveyed.
Explanation:To estimate the current percentage of U.S. adults who use the Internet with a 95 percent confidence level and an error margin of no more than three percentage points, we must determine the sample size we need to survey. We'll follow the formula below for estimating the sample size:
n = (Z² * p(1-p)) / E^2
Where n is the sample size, Z is the z-score associated with our desired confidence level (for a 95% confidence level, Z is about 1.96), p is the estimated proportion of the population (based on the 2006 data, we'll use 0.73), and E is the margin of error (which we want to be 0.03).
Plug in the values:
n = (1.96² * 0.73 * 0.27) / 0.03² = 1067.14
Since we cannot survey a fraction of a person, we round up to the next whole number. Therefore, the manager would need to survey 1068 adults in order to be 95 percent confident that the sample percentage is in error by no more than three percentage points.
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A survey was conducted at two colleges. 500 students at College A participated in the study. The results indicated that on average, the students spent 15 hours per week doing online assignments and its standard deviation was 5 hours. At College B, 400 students participated in the study. The average hours they worked for online assignments was 20 with a standard deviation of 4 hours. Please test whether there is a true difference in the time students spent for online assignments between the two colleges (using a confidence level of 99%).
Answer:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
Step-by-step explanation:
Data given
[tex]\bar X_{1}=15[/tex] represent the mean for sample A
[tex]\bar X_{2}=20[/tex] represent the mean for sample B
[tex]s_{1}=5[/tex] represent the sample standard deviation for A
[tex]s_{f}=4[/tex] represent the sample standard deviation for B
[tex]n_{1}=500[/tex] sample size for the group A
[tex]n_{2}=400[/tex] sample size for the group B
[tex]\alpha=0.01[/tex] Significance level provided
t would represent the statistic
System of hypothesis
The system of hypothesis is the true difference in the time students spent for online assignments between the two colleges, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]
Since we don't know the deviations the statistic is given by:
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
The degrees of freedom are given by [tex]df=n_1 +n_2 -2=500+400-2=898[/tex]
Replacing the info given we got:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
Haala buys 13 identical shirts and 22 identical ties for £363.01
The cost of a shirt is £15.35
Find the cost of a tie.
Answer:
£7.43
Step-by-step explanation:
The total cost is ...
13s +22t = 363.01
13(15.35) +22t = 363.01 . . . . fill in the cost of a shirt
22t = 163.46 . . . . . . . . . . . . . subtract 199.55
t = 7.43 . . . . . . . . . . . divide by 22
The cost of a tie is £7.43.
g According to a New York Times/CBS News poll conducted during June 24–28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of 1810 American adults, 62% said that owning a home is a very important part of the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a 2% significance level, and use both the p-value and the critical-value approaches.
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
a) For the null hypothesis,
P = 0.55
For the alternative hypothesis,
P > 0.55
Considering the population proportion, probability of success, p = 0.55
q = probability of failure = 1 - p
q = 1 - 0.55 = 0.45
Considering the sample,
Probability of success, P = 0.62
Number of samples, n = 1810
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.62 - 0.55)/√(0.55 × 0.45)/1810 = 5.98
Since this is a right tailed test, the critical value would be the p value to the right of z = 5.98
p value = 0.00001
Since alpha, 0.02 > than the p value, 0.00001, then we would reject the null hypothesis.
Using the critical value approach, By using the critical region method,
the calculated test statistic is 5.98 for the right tail and - 5.98 for the left tail
Since α = 0.02, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.02/2 = 0.01
The z score for an area to the left of 0.01 is - 2.325
For the right, α/2 = 1 - 0.01 = 0.99
The z score for an area to the right of 0.995 is 2.325
In order to reject the null hypothesis, the test statistic must be smaller than - 2.325 or greater than 2.325
Since - 5.98 < - 2.325 and 5.98 > 2.325, we would reject the null hypothesis.
Therefore, it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%.
Let's take the speed of sound to be 340 m/s. What would be the length of the pipe in a pipe organ that produces a note with a pitch of 170
Hz?
Answer:
L = 2 m
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m
Step-by-step explanation:
Given;
Speed of sound v = 340 m/s
Frequency of sound f = 170 hz
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is;
Length L = v/f = speed/frequency
L = 340/170
L = 2 m
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m
A new alloy is made by mixing 72 grams of iron with 9 grams of zinc. How many grams of iron are required to make the alloy when combined with 144 grams of zinc?
A) 992 grams
B) 1,152 grams
C) 1,226 grams
D) 1,445 grams
Answer:
B) 1,152 grams
Step-by-step explanation:
which value for x makes the sentence true
1/8(x-56)=7/8
Answer:
63.
Step-by-step explanation:
To solve this equation, we will first need to multiply both sides by 8 to get rid of the coefficient:
8×[tex]\frac{1}{8}[/tex](x-56)=[tex]\frac{7}{8}[/tex]×8
Now, this will get rid of the fractions, giving us:
x-56= 7
Next, simply add 56 to both sides:
x-56+56= 7+56
This results in:
x=63.