Question 1

Find and Interpret the Area under a Normal Curve
-more than $\$ 153,800$ if the standard deviation is $\$ 1900$.

Accepted Answer

A)  $2.5 \%$ 
B)  $97.5 \%$ 
C)  $47.5 \%$ 
D)  $95 \%$ 
A)  $2.5 \%$ 
B)  $97.5 \%$ 
C)  $47.5 \%$ 
D)  $95 \%$

Question 2

Find z-scores for a Given Area
-Find the $z$-score that is less than the mean and for which $70 \%$ of the distribution's area lies to its right.

Accepted Answer

A)  $- 0.53$ 
B)  $- 0.98$ 
C)  $- 0.81$ 
D)  $- 0.47$ 
A)  $- 0.53$ 
B)  $- 0.98$ 
C)  $- 0.81$ 
D)  $- 0.47$

Question 3

Find the Value of a Normal Random Variable
-The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.0 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.

Accepted Answer

A)  4.7 min 
B)  4.5 min 
C)  4.3 min 
D)  4.8 min 
A)  4.7 min 
B)  4.5 min 
C)  4.3 min 
D)  4.8 min

Question 4

Approximate Binomial Probabilities Using the Normal Distribution
-Find the probability that in 200 tosses of a fair six-sided die, a three will be obtained at least 40 times.

Accepted Answer

A)  0.1210 
B)  0.8810 
C)  0.0871 
D)  0.3875 
A)  0.1210 
B)  0.8810 
C)  0.0871 
D)  0.3875

Question 5

A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is
as given.
-$$X = 72 ; \sigma = 3$$

Accepted Answer

A)  4 
B)  12 
C)  5 
D)  3 
A)  4 
B)  12 
C)  5 
D)  3

Question 6

Find and Interpret the Area under a Normal Curve
-Use the standard normal distribution to find $\mathrm { P } ( - 2.50 < \mathrm { z } < 1.50 )$.

Accepted Answer

A)  $0.9270$ 
B)  $0.8822$ 
C)  $0.6167$ 
D)  $0.5496$ 
A)  $0.9270$ 
B)  $0.8822$ 
C)  $0.6167$ 
D)  $0.5496$

Question 7

Find the Value of a Normal Random Variable
-The board of examiners that administers the real estate broker s examination in a certain state found that the mean score on the test was 451 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score Assume that the scores are normally distributed.

Accepted Answer

Let @#LAT-DLM& be a score on this exam. Then @#LAT-DLM& is a

Question 8

Find and Interpret the Area under a Normal Curve
-A firm believes the internal rate of return for its proposed investment can best be described by a normal distribution with mean 24% and standard deviation 3%. What is the probability that the internal rate of return for the investment will be at least 19.5%

Accepted Answer

Let @#LAT-DLM& be the internal rate of return. The

Question 9

Find the Value of a Normal Random Variable
-The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.12 ounce. Every can that has more than 12.30 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that need to be cleaned because of spillage to 3%

Accepted Answer

A)  12.0744 oz 
B)  12.5256 oz 
C)  12.0396 oz 
D)  12.5604 oz 
A)  12.0744 oz 
B)  12.5256 oz 
C)  12.0396 oz 
D)  12.5604 oz

Question 10

Approximate Binomial Probabilities Using the Normal Distribution
-Assuming that all conditions are met to approximate a binomial probability distribution with the standard normal distribution, then to compute $P ( 12 \leq x \leq 15 )$ from the binomial distribution we must compute _____as the normal approximation.

Accepted Answer

A)  $\mathrm { P } ( 11.5  15.5 )$ and $\mathrm { P } ( \mathrm { x }  12.5 )$ and $\mathrm { P } ( \mathrm { x } < 14.5 )$ 
A)  $\mathrm { P } ( 11.5  15.5 )$ and $\mathrm { P } ( \mathrm { x }  12.5 )$ and $\mathrm { P } ( \mathrm { x } < 14.5 )$

Question 11

Approximate Binomial Probabilities Using the Normal Distribution
-In a recent survey, 84% of the community favored building more parks in their neighborhood. You randomly select 18 citizens and ask each if he or she thinks the community needs more parks. Decide whether you can use the normal distribution to approximate the binomial distribution. If so, find the mean and standard deviation. If not, explain why.

Accepted Answer

cannot use normal di

Question 12

Find z-scores for a Given Area
-Find the $z$-scores for which $90 \%$ of the distribution's area lies between $- z$ and $z$.

Accepted Answer

A)  $( - 1.645,1.645 )$ 
B)  $( - 2.33,2.33 )$ 
C)  $( - 1.96,1.96 )$ 
D)  $( - 0.99,0.99 )$ 
A)  $( - 1.645,1.645 )$ 
B)  $( - 2.33,2.33 )$ 
C)  $( - 1.96,1.96 )$ 
D)  $( - 0.99,0.99 )$

Question 13

A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is
as given.
-$$X = 68 ; \sigma = 8$$

Accepted Answer

A)  1 
B)  8 
C)  68 
D)  $\frac { 15 } { 2 }$ 
A)  1 
B)  8 
C)  68 
D)  $\frac { 15 } { 2 }$

Question 14

Interpret the Area under the Standard Normal Curve as a Probability
-Use the standard normal distribution to find $\mathrm { P } ( 0 < \mathrm { Z } < 2.25 )$.

Accepted Answer

A)  $0.4878$ 
B)  $0.5122$ 
C)  $0.8817$ 
D)  $0.7888$ 
A)  $0.4878$ 
B)  $0.5122$ 
C)  $0.8817$ 
D)  $0.7888$

Question 15

Provide an appropriate response
-High temperatures in a certain city for the month of August follow a uniform distribution over the interval 65°F to 87°F. What is the probability that a randomly selected August day has a high temperature that exceeded 70°F

Accepted Answer

A)  0.7727 
B)  0.2273 
C)  0.4605 
D)  0.0455 
A)  0.7727 
B)  0.2273 
C)  0.4605 
D)  0.0455

Question 16

Find the Area under the Standard Normal Curve
-Find the area under the standard normal curve between $\mathrm { z } = - 1.25$ and $\mathrm { z } = 1.25$.

Accepted Answer

A)  $0.7888$ 
B)  $0.8817$ 
C)  $0.6412$ 
D)  $0.2112$ 
A)  $0.7888$ 
B)  $0.8817$ 
C)  $0.6412$ 
D)  $0.2112$

Question 17

Interpret the Area under the Standard Normal Curve as a Probability
-Scores on a standardized test are normally distributed with a mean of 104 and a standard deviation of 20 . An individual's test score is found to be 109 . Find the $\mathrm { z }$-score corresponding to this value.

Accepted Answer

A)  $0.25$ 
B)  $- 0.25$ 
C)  $4.00$ 
D)  $- 4.00$ 
A)  $0.25$ 
B)  $- 0.25$ 
C)  $4.00$ 
D)  $- 4.00$

Question 18

Use Normal Probability Plots to Assess Normality
-Determine whether the following normal probability plot indicates that the sample data could have come from a population that is normally distributed.

Accepted Answer

A)  normally distributed 
B)  not normally distributed 
A)  normally distributed 
B)  not normally distributed

Question 19

Use Normal Probability Plots to Assess Normality
-If sample data are taken from a population that is normally distributed, a normal probability plot of the observed data values versus the expected z scores will

Accepted Answer

A)  be approximately linear. 
B)  have no discernable pattern. 
C)  look exponential in nature. 
D)  have a correlation coefficient near 0. 
A)  be approximately linear. 
B)  have no discernable pattern. 
C)  look exponential in nature. 
D)  have a correlation coefficient near 0.

Question 20

Find the Area under the Standard Normal Curve
-Find the area under the standard normal curve to the left of $\mathrm { z } = 1.25$.

Accepted Answer

A)  $0.8944$ 
B)  $0.1056$ 
C)  $0.2318$ 
D)  $0.7682$ 
A)  $0.8944$ 
B)  $0.1056$ 
C)  $0.2318$ 
D)  $0.7682$

Find and Interpret the Area under a Normal Curve -more than $\$ 153,800$ if the standard deviation is $\$ 1900$ .

Find z-scores for a Given Area -Find the $z$ -score that is less than the mean and for which $70 \%$ of the distribution's area lies to its right.

Approximate Binomial Probabilities Using the Normal Distribution -Find the probability that in 200 tosses of a fair six-sided die, a three will be obtained at least 40 times.

A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is as given. - $X = 72 ; \sigma = 3$

Find and Interpret the Area under a Normal Curve -Use the standard normal distribution to find $\mathrm { P } ( - 2.50 < \mathrm { z } < 1.50 )$ .

Find z-scores for a Given Area -Find the $z$ -scores for which $90 \%$ of the distribution's area lies between $- z$ and $z$ .

A random variable X is normally distributed with = 60. Convert the value of X to a z-score, if the standard deviation is as given. - $X = 68 ; \sigma = 8$

Interpret the Area under the Standard Normal Curve as a Probability -Use the standard normal distribution to find $\mathrm { P } ( 0 < \mathrm { Z } < 2.25 )$ .

Provide an appropriate response -High temperatures in a certain city for the month of August follow a uniform distribution over the interval 65°F to 87°F. What is the probability that a randomly selected August day has a high temperature that exceeded 70°F

Find the Area under the Standard Normal Curve -Find the area under the standard normal curve between $\mathrm { z } = - 1.25$ and $\mathrm { z } = 1.25$ .

Interpret the Area under the Standard Normal Curve as a Probability -Scores on a standardized test are normally distributed with a mean of 104 and a standard deviation of 20 . An individual's test score is found to be 109 . Find the $\mathrm { z }$ -score corresponding to this value.

Use Normal Probability Plots to Assess Normality -Determine whether the following normal probability plot indicates that the sample data could have come from a population that is normally distributed.

Use Normal Probability Plots to Assess Normality -If sample data are taken from a population that is normally distributed, a normal probability plot of the observed data values versus the expected z scores will

Find the Area under the Standard Normal Curve -Find the area under the standard normal curve to the left of $\mathrm { z } = 1.25$ .

Data Collection

Creating Tables and Drawing Pictures of Data

Numerically Summarizing Data

Describing the Relation Between Two Variables

Probability

Discrete Probability Distributions

Sampling Distributions

Estimating the Value of a Parameter Using Confidence Intervals

Hypothesis Tests Regarding a Parameter

Inference on Two Samples

Inference on Categorical Data

Comparing Three or More Means

Inference of the Least-Squares Regression Model and Multiple Regression

Nonparametric Statistics

Filters

Exam 7: The Normal Probability Distribution

Find and Interpret the Area under a Normal Curve -more than $153,800\$ 153,800$153,800 if the standard deviation is $1900\$ 1900$1900 .

Find z-scores for a Given Area -Find the zzz -score that is less than the mean and for which 70%70 \%70% of the distribution's area lies to its right.