Question 1

Which of the following properties distinguishes the standard normal distribution from other normal distributions?

Accepted Answer

A)  The mean is 0 and the standard deviation is 1. 
B)  The mean is located at the center of the distribution. 
C)  The total area under the curve is equal to 1.00. 
D)  The curve is continuous. 
A)  The mean is 0 and the standard deviation is 1. 
B)  The mean is located at the center of the distribution. 
C)  The total area under the curve is equal to 1.00. 
D)  The curve is continuous.

Question 2

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the
Probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

Accepted Answer

A)  15.7% 
B)  44.5% 
C)  6.4% 
D)  28.8% 
A)  15.7% 
B)  44.5% 
C)  6.4% 
D)  28.8%

Question 3

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

Accepted Answer

A)  -1.46 
B)  1.46 
C)  1.23 
D)  0.07 
A)  -1.46 
B)  1.46 
C)  1.23 
D)  0.07

Question 4

Use the normal approximation to find the indicated probability. The sample size is $n$, the population proportion of successes is $p$, and $X$ is the number of successes in the sample.
$$n = 75 , p = 0.52 : P ( 34 \leq X \leq 47 )$$

Accepted Answer

A)  0.0250 
B)  0.1020 
C)  0.9750 
D)  0.8730 
A)  0.0250 
B)  0.1020 
C)  0.9750 
D)  0.8730

Question 5

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.
$$n = 78 , p = 0.75 : P ( X < 68 )$$

Accepted Answer

A)  0.9906 
B)  0.0094 
C)  0.9890 
D)  0.9920 
A)  0.9906 
B)  0.0094 
C)  0.9890 
D)  0.9920

Question 6

$$\text { The probability } P ( 0 < z < 0.97 ) \text { is } 0.3340 \text {. }$$

Accepted Answer

A) True 
 B)False

Question 7

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will
Build to satisfy the middle 80% of the market. Assume that the variable is normally
Distributed.

Accepted Answer

A)  $230,900 and $256,100 
B)  $242,000 and $245,000 
C)  $230,000 and $257,000 
D)  $224,300 and $262,700 
A)  $230,900 and $256,100 
B)  $242,000 and $245,000 
C)  $230,000 and $257,000 
D)  $224,300 and $262,700

Question 8

If a normal distribution has a mean of 35 and a standard deviation of 10, then

Accepted Answer

A)  the median is 35 and the mode is 35. 
B)  the median is 45 and the mode is 
C)  the median is 25 and the mode is 45. 
D)  the median is 35 and the mode is 
A)  the median is 35 and the mode is 35. 
B)  the median is 45 and the mode is 
C)  the median is 25 and the mode is 45. 
D)  the median is 35 and the mode is

Question 9

$X$ is a normally distributed random variable with a standard deviation of $3.50$. Find the mean of $X$ when $64.8 \%$ of the area lies to the left of $5.33$. (Note: the diagram is not necessarily to scale.)

Accepted Answer

A)  3.7 
B)  2.1 
C)  4.0 
D)  5.2 
A)  3.7 
B)  2.1 
C)  4.0 
D)  5.2

Question 10

$$\text { Find the probability } P ( z > 0.78 ) \text { using the standard normal distribution. }$$

Accepted Answer

A)  0.2823 
B)  0.7177 
C)  0.2177 
D)  0.7823 
A)  0.2823 
B)  0.7177 
C)  0.2177 
D)  0.7823

Question 11

For a normal distribution curve with a mean of 9 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to
A probability of approximately 34%?

Accepted Answer

A)  from 9 to 14 
B)  from 4 to 14 
C)  from 6.5 to 11.5 
D)  from -1 to 19 
A)  from 9 to 14 
B)  from 4 to 14 
C)  from 6.5 to 11.5 
D)  from -1 to 19

Question 12

The normal distribution curve can be used as a probability distribution curve for
normally distributed variables.

Accepted Answer

A) True 
 B)False

Question 13

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability
That a tree is less than 12.5 feet tall.

Accepted Answer

A)  0.82 
B)  0.96 
C)  0.91 
D)  0.73 
A)  0.82 
B)  0.96 
C)  0.91 
D)  0.73

Question 14

When the majority of the data values fall to the right of the mean, the distribution is said
to be left-skewed.

Accepted Answer

A) True 
 B)False

Question 15

The number of standard deviations a particular X value is from the mean is commonly referred to as .

Accepted Answer

A)  $\sigma ^ { 2 }$ 
B)  $z$ 
C)  $\mu$ 
D)  $P ( X )$ 
A)  $\sigma ^ { 2 }$ 
B)  $z$ 
C)  $\mu$ 
D)  $P ( X )$

Question 16

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation
Of 200, what is the lowest possible score a student needs to qualify for acceptance into
The university?

Accepted Answer

A)  1250 
B)  1100 
C)  1330 
D)  1400 
A)  1250 
B)  1100 
C)  1330 
D)  1400

Question 17

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a $z$ value of

Accepted Answer

A)  -3 
B)  -4 
C)  -2 
D)  0 
A)  -3 
B)  -4 
C)  -2 
D)  0

Question 18

$$\text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = - 2.16 \text {. }$$

Accepted Answer

A)  0.3708 
B)  0.4846 
C)  0.9846 
D)  -2.1600 
A)  0.3708 
B)  0.4846 
C)  0.9846 
D)  -2.1600

Question 19

$$\text { Find the probability } P ( z > - 0.54 ) \text { using the standard normal distribution. }$$

Accepted Answer

A)  0.2946 
B)  0.7946 
C)  0.7054 
D)  0.2054 
A)  0.2946 
B)  0.7946 
C)  0.7054 
D)  0.2054

Question 20

A gardener buys a package of seeds. Eighty-one percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probability that the number of seeds that
Germinate is between 89.2 and 105.2 exclusive.

Accepted Answer

A)  0.0801 
B)  0.0401 
C)  0.9599 
D)  0.9199 
A)  0.0801 
B)  0.0401 
C)  0.9599 
D)  0.9199

Which of the following properties distinguishes the standard normal distribution from other normal distributions?

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the Probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

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

Use the normal approximation to find the indicated probability. The sample size is $n$ , the population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 75 , p = 0.52 : P ( 34 \leq X \leq 47 )$

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. $n = 78 , p = 0.75 : P ( X < 68 )$

$\text { The probability } P ( 0 < z < 0.97 ) \text { is } 0.3340 \text {. }$

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will Build to satisfy the middle 80% of the market. Assume that the variable is normally Distributed.

If a normal distribution has a mean of 35 and a standard deviation of 10, then

$\text { Find the probability } P ( z > 0.78 ) \text { using the standard normal distribution. }$

For a normal distribution curve with a mean of 9 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to A probability of approximately 34%?

The normal distribution curve can be used as a probability distribution curve for normally distributed variables.

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability That a tree is less than 12.5 feet tall.

When the majority of the data values fall to the right of the mean, the distribution is said to be left-skewed.

The number of standard deviations a particular X value is from the mean is commonly referred to as .

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation Of 200, what is the lowest possible score a student needs to qualify for acceptance into The university?

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a $z$ value of

$\text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = - 2.16 \text {. }$ $\text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = - 2.16 \text {. }$

$\text { Find the probability } P ( z > - 0.54 ) \text { using the standard normal distribution. }$

A gardener buys a package of seeds. Eighty-one percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probability that the number of seeds that Germinate is between 89.2 and 105.2 exclusive.

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

Which of the following properties distinguishes the standard normal distribution from other normal distributions?

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the Probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

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.

Use the normal approximation to find the indicated probability. The sample size is nnn , the population proportion of successes is ppp , and XXX is the number of successes in the sample. n=75,p=0.52:P(34≤X≤47)n = 75 , p = 0.52 : P ( 34 \leq X \leq 47 )n=75,p=0.52:P(34≤X≤47)

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=78,p=0.75:P(X<68)n = 78 , p = 0.75 : P ( X < 68 )n=78,p=0.75:P(X<68)

The probability P(0<z<0.97) is 0.3340. \text { The probability } P ( 0 < z < 0.97 ) \text { is } 0.3340 \text {. } The probability P(0<z<0.97) is 0.3340.

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will Build to satisfy the middle 80% of the market. Assume that the variable is normally Distributed.

If a normal distribution has a mean of 35 and a standard deviation of 10, then

XXX is a normally distributed random variable with a standard deviation of 3.503.503.50 . Find the mean of XXX when 64.8%64.8 \%64.8% of the area lies to the left of 5.335.335.33 . (Note: the diagram is not necessarily to scale.)

Find the probability P(z>0.78) using the standard normal distribution. \text { Find the probability } P ( z > 0.78 ) \text { using the standard normal distribution. } Find the probability P(z>0.78) using the standard normal distribution.

For a normal distribution curve with a mean of 9 and a standard deviation of 5, which of the following ranges of the variable will define an area under the curve corresponding to A probability of approximately 34%?

The normal distribution curve can be used as a probability distribution curve for normally distributed variables.

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability That a tree is less than 12.5 feet tall.

When the majority of the data values fall to the right of the mean, the distribution is said to be left-skewed.

The number of standard deviations a particular X value is from the mean is commonly referred to as .

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation Of 200, what is the lowest possible score a student needs to qualify for acceptance into The university?

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a zzz value of

Find the area under the standard normal distribution curve between z=0 and z=−2.16. \text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = - 2.16 \text {. } Find the area under the standard normal distribution curve between z=0 and z=−2.16.

Find the probability P(z>−0.54) using the standard normal distribution. \text { Find the probability } P ( z > - 0.54 ) \text { using the standard normal distribution. } Find the probability P(z>−0.54) using the standard normal distribution.

A gardener buys a package of seeds. Eighty-one percent of seeds of this type germinate. The gardener plants 120 seeds. Approximate the probability that the number of seeds that Germinate is between 89.2 and 105.2 exclusive.

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

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

Use the normal approximation to find the indicated probability. The sample size is $n$ , the population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 75 , p = 0.52 : P ( 34 \leq X \leq 47 )$

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. $n = 78 , p = 0.75 : P ( X < 68 )$

$\text { The probability } P ( 0 < z < 0.97 ) \text { is } 0.3340 \text {. }$

$\text { Find the probability } P ( z > 0.78 ) \text { using the standard normal distribution. }$

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a $z$ value of

$\text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = - 2.16 \text {. }$ $\text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = - 2.16 \text {. }$

$\text { Find the probability } P ( z > - 0.54 ) \text { using the standard normal distribution. }$