Exam 6: The Normal Distribution

The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find The probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon.

(Multiple Choice)

4.7/5

(86)

Question 21

$\text { Find the probability } P ( z < - 0.31 ) \text { using the standard normal distribution. }$

(Multiple Choice)

4.8/5

(70)

Question 22

$\text { Find the } z \text { value that corresponds to the given area. }$ $\text { Find the } z \text { value that corresponds to the given area. }$

(Multiple Choice)

4.8/5

(85)

Question 23

$\text { Find the probability } P ( z < 0.37 ) \text { using the standard normal distribution. }$

(Multiple Choice)

4.8/5

(99)

Question 24

$\text { Find the area under the standard normal curve to the right of } z = 2 \text {. }$

(Multiple Choice)

4.7/5

(76)

Question 25

On an easy test, the mean score was 96 out of a possible 100 points. The distribution of the test scores is likely to be

(Multiple Choice)

4.9/5

(83)

Question 26

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability That the average mileage of the fleet is greater than 33.5 mpg?

(Multiple Choice)

4.9/5

(77)

Question 27

A sample of size 52 will be drawn from a population with mean 18 and standard deviation 13. Find the probability that $\bar { x }$ will be less than 21 .

(Multiple Choice)

4.7/5

(85)

Question 28

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 77 , p = 0.33 : P ( X \leq 18 )$

(Multiple Choice)

4.9/5

(81)

Question 29

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

(Multiple Choice)

4.9/5

(77)

Question 30

The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%.

(True/False)

4.9/5

(70)

Question 31

A sample of size 65 will be drawn from a population with mean 22 and standard deviation 15 . Find the probability that $\bar { x }$ will be between 20 and 25 .

(Multiple Choice)

4.8/5

(82)

Question 32

The difference between a sample mean and the population mean may be referred to as .

(Multiple Choice)

4.9/5

(82)

Question 33

Find the area under the standard normal curve that lies outside the interval between $z = - 0.6$ and $z = 1.8$ .

(Multiple Choice)

4.9/5

(79)

Question 34

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

(Multiple Choice)

4.8/5

(75)

Question 35

A normal population has a mean $\mu = 33$ and standard deviation $\sigma = 9$ . What is the probability that a randomly chosen value will be greater than 44 ?

(Multiple Choice)

4.9/5

(82)

Question 36

A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will Admit to reading the newspaper while driving.

(Multiple Choice)

4.8/5

(89)

Question 37

The average age of doctors in a certain hospital is 45.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 8.0 years. If 9 doctors are Chosen at random for a committee, find the probability that the average age of those Doctors is less than 46.9 years. Assume that the variable is normally distributed.

(Multiple Choice)

4.9/5

(81)

Question 38

A biologist estimates that 70% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have This tick?

(Multiple Choice)

4.8/5

(72)

Question 39

The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast Food restaurant is selected at random, what is the probability that the worker earns more Than $6.75?

(Multiple Choice)

4.9/5

(87)

Question 40

The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find The probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon.

$\text { Find the probability } P ( z < - 0.31 ) \text { using the standard normal distribution. }$

$\text { Find the } z \text { value that corresponds to the given area. }$ $\text { Find the } z \text { value that corresponds to the given area. }$

$\text { Find the probability } P ( z < 0.37 ) \text { using the standard normal distribution. }$

$\text { Find the area under the standard normal curve to the right of } z = 2 \text {. }$

On an easy test, the mean score was 96 out of a possible 100 points. The distribution of the test scores is likely to be

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability That the average mileage of the fleet is greater than 33.5 mpg?

A sample of size 52 will be drawn from a population with mean 18 and standard deviation 13. Find the probability that $\bar { x }$ will be less than 21 .

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 77 , p = 0.33 : P ( X \leq 18 )$

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%.

A sample of size 65 will be drawn from a population with mean 22 and standard deviation 15 . Find the probability that $\bar { x }$ will be between 20 and 25 .

The difference between a sample mean and the population mean may be referred to as .

Find the area under the standard normal curve that lies outside the interval between $z = - 0.6$ and $z = 1.8$ .

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

A normal population has a mean $\mu = 33$ and standard deviation $\sigma = 9$ . What is the probability that a randomly chosen value will be greater than 44 ?

A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will Admit to reading the newspaper while driving.

A biologist estimates that 70% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have This tick?

The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast Food restaurant is selected at random, what is the probability that the worker earns more Than $6.75?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Nonparametric Statistics

Sampling and Simulation

Filters

Exam 6: The Normal Distribution

The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find The probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon.

Find the probability P(z<−0.31) using the standard normal distribution. \text { Find the probability } P ( z < - 0.31 ) \text { using the standard normal distribution. } Find the probability P(z<−0.31) using the standard normal distribution.

Find the z value that corresponds to the given area. \text { Find the } z \text { value that corresponds to the given area. } Find the z value that corresponds to the given area.

Find the probability P(z<0.37) using the standard normal distribution. \text { Find the probability } P ( z < 0.37 ) \text { using the standard normal distribution. } Find the probability P(z<0.37) using the standard normal distribution.

Find the area under the standard normal curve to the right of z=2. \text { Find the area under the standard normal curve to the right of } z = 2 \text {. } Find the area under the standard normal curve to the right of z=2.

On an easy test, the mean score was 96 out of a possible 100 points. The distribution of the test scores is likely to be

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability That the average mileage of the fleet is greater than 33.5 mpg?

A sample of size 52 will be drawn from a population with mean 18 and standard deviation 13. Find the probability that xˉ\bar { x }xˉ will be less than 21 .

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is ppp , and XXX is the number of successes in the sample. n=77,p=0.33:P(X≤18)n = 77 , p = 0.33 : P ( X \leq 18 )n=77,p=0.33:P(X≤18)

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%.

A sample of size 65 will be drawn from a population with mean 22 and standard deviation 15 . Find the probability that xˉ\bar { x }xˉ will be between 20 and 25 .

The difference between a sample mean and the population mean may be referred to as .

Find the area under the standard normal curve that lies outside the interval between z=−0.6z = - 0.6z=−0.6 and z=1.8z = 1.8z=1.8 .

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

A normal population has a mean μ=33\mu = 33μ=33 and standard deviation σ=9\sigma = 9σ=9 . What is the probability that a randomly chosen value will be greater than 44 ?

A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will Admit to reading the newspaper while driving.

A biologist estimates that 70% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 216 or fewer deer have This tick?

The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast Food restaurant is selected at random, what is the probability that the worker earns more Than $6.75?

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Analysis of Variance

Nonparametric Statistics

Sampling and Simulation

Filters

$\text { Find the probability } P ( z < - 0.31 ) \text { using the standard normal distribution. }$

$\text { Find the } z \text { value that corresponds to the given area. }$ $\text { Find the } z \text { value that corresponds to the given area. }$

$\text { Find the probability } P ( z < 0.37 ) \text { using the standard normal distribution. }$

$\text { Find the area under the standard normal curve to the right of } z = 2 \text {. }$

A sample of size 52 will be drawn from a population with mean 18 and standard deviation 13. Find the probability that $\bar { x }$ will be less than 21 .

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 77 , p = 0.33 : P ( X \leq 18 )$

A sample of size 65 will be drawn from a population with mean 22 and standard deviation 15 . Find the probability that $\bar { x }$ will be between 20 and 25 .

Find the area under the standard normal curve that lies outside the interval between $z = - 0.6$ and $z = 1.8$ .

A normal population has a mean $\mu = 33$ and standard deviation $\sigma = 9$ . What is the probability that a randomly chosen value will be greater than 44 ?