Deck 7: The Normal Probability Distribution

Question 1

State the Properties of the Normal Curve

Answer 1

A

Question 2

State the Properties of the Normal Curve
The normal density curve is symmetric about

A) Its mean
B) The horizontal axis
C) An inflection point
D) A point located one standard deviation from the mean

Answer 2

A

Question 3

Provide an appropriate response
A random number generator is set top generate integer random numbers between 1 and 10 inclusive following a uniform distribution. What is the probability of the random number generator generating a 7

A) 0.7
B) 0
C) 0.07
D) 0.5

Answer 3

A

Question 4

Provide an appropriate response
A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 4.5 to 7.5 gallons per minute. Find the probability that between 5.0 gallons and 6.0 gallons are pumped during a randomly selected minute.

A) 0.33
B) 0.67
C) 0
D) 1

Question 5

Explain the Role of Area in the Normal Density Function

Question 6

State the Properties of the Normal Curve

Question 7

Explain the Role of Area in the Normal Density Function

Question 8

Provide an appropriate response
Suppose x is a uniform random variable with c = 10 and d = 90. Find the probability that a randomly selected observation exceeds 26.

A) 0.8
B) 0.2
C) 0.1
D) 0.9

Question 9

Provide an appropriate response
High temperatures in a certain city for the month of August follow a uniform distribution over the interval 64°F to 94°F. Find the high temperature which 90% of the August days exceed.

A) 67°F
B) 91°F
C) 74°F
D) 94°F

Question 10

Provide an appropriate response
Suppose a uniform random variable can be used to describe the outcome of an experiment with the outcomes ranging from 10 to 70. What is the probability that this experiment results in an outcome less than 20

A) 0.17
B) 0.13
C) 0.22
D) 1

Question 11

State the Properties of the Normal Curve

Question 12

Graph a Normal Curve
Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would

A) Have the same height but one would be shifted 4 units to the right.
B) Have the same height but one would be shifter 4 units to the left.
C) Have no horizontal displacement but one would be steeper that the other.
D) Have no horizontal displacement but one would be flatter than the other.

Question 13

Provide an appropriate response
Suppose x is a uniform random variable with c = 30 and d = 70. Find the probability that a randomly selected observation is between 33 and 65.

A) 0.80
B) 0.20
C) 0.5
D) 0.8

Question 14

Provide an appropriate response
In a uniform probability distribution, any random variable is just as likely as any other random variable to occur, provided the random variables belong to the distribution.

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

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

Question 16

State the Properties of the Normal Curve

Question 17

Graph a Normal Curve
Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 0 and standard deviation of 0.5. The graphs would

A) Have no horizontal displacement but one would be steeper that the other.
B) Have no horizontal displacement but one would be flatter than the other.
C) Have the same height but one would be shifted 4 units to the right.
D) Have the same height but one would be shifter 4 units to the left.

Question 18

Provide an appropriate response
The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 6.5 to 8.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 7.4 millimeters

A) 0.55
B) 0.8706
C) 3.5
D) 0.4933

Question 19

Explain the Role of Area in the Normal Density Function

Question 20

Graph a Normal Curve
You are performing a study about the weight of preschoolers. A previous study found the weights to be normally distributed with a mean of 30 and a standard deviation of 4. You randomly sample 30 preschool children and find their weights to be as follows. a) Draw a histogram to display the data. Is it reasonable to assume that the weights are normally distributed Why b) Find the mean and standard deviation of your sample. c) Is there a high probability that the mean and standard deviation of your sample are consistent with those found in previous studies Explain your reasoning.

Question 21

Find the Area under the Standard Normal Curve

Question 22

Explain the Role of Area in the Normal Density Function
The area under the normal curve drawn with regard to the population parameters is the same as the proportion of the population that has these characteristics.

Question 23

Find the Area under the Standard Normal Curve

Question 24

Find the Area under the Standard Normal Curve

Question 25

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.

Question 26

Find the Area under the Standard Normal Curve

Question 27

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.

Question 28

Find the Area under the Standard Normal Curve

Question 29

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.

Question 30

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.

Question 31

Find the Area under the Standard Normal Curve

Question 32

Explain the Role of Area in the Normal Density Function
The proportion of the population that has certain characteristics is the same as the probability that a randomly selected individual of the population has these same characteristics.

Question 33

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.

Question 34

Explain the Role of Area in the Normal Density Function
The area under the normal curve drawn with regard to the population parameters is the same as the probability that a randomly selected individual of a population has these characteristics.

Question 35

Find the Area under the Standard Normal Curve

Question 36

Find the Area under the Standard Normal Curve

Question 37

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.

Question 38

Find the Area under the Standard Normal Curve

Question 39

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.

Question 40

Find the Area under the Standard Normal Curve

Question 41

Interpret the Area under the Standard Normal Curve as a Probability

Question 42

Interpret the Area under the Standard Normal Curve as a Probability

Question 43

Interpret the Area under the Standard Normal Curve as a Probability

Question 44

Interpret the Area under the Standard Normal Curve as a Probability

Question 45

Interpret the Area under the Standard Normal Curve as a Probability

Question 46

Interpret the Area under the Standard Normal Curve as a Probability

Question 47

Find the Area under the Standard Normal Curve

Question 48

Find z-scores for a Given Area

Question 49

Find z-scores for a Given Area

Question 50

Interpret the Area under the Standard Normal Curve as a Probability

Question 51

Find and Interpret the Area under a Normal Curve

Question 52

Find z-scores for a Given Area

Question 53

Find z-scores for a Given Area

Question 54

Interpret the Area under the Standard Normal Curve as a Probability

Question 55

Interpret the Area under the Standard Normal Curve as a Probability

Question 56

Find z-scores for a Given Area

Question 57

Interpret the Area under the Standard Normal Curve as a Probability

Question 58

Interpret the Area under the Standard Normal Curve as a Probability

Question 59

Find z-scores for a Given Area

Question 60

Find z-scores for a Given Area

Question 61

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 36% and standard deviation 3%. What is the probability that the internal rate of return for the investment exceeds 42%

Question 62

Find and Interpret the Area under a Normal Curve

Question 63

Find and Interpret the Area under a Normal Curve
Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean equal to 440 tomatoes per day and a standard deviation equal to 30 tomatoes per day. If there are 398 tomatoes available to be sold at the roadside stand at the beginning of a day, what is the probability that they will all be sold

Question 64

Find and Interpret the Area under a Normal Curve
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.12 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12.02 and 12.08 ounces.

A) 0.1525
B) 0.8351
C) 0.1649
D) 0.8475

Question 65

Find and Interpret the Area under a Normal Curve
The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.18 ounce. The cans only hold 12.45 ounces of soda. Every can that has more than 12.45 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 probability a randomly selected can will need to go through this process

A) 0.1587
B) 0.3413
C) 0.8413
D) 0.6587

Question 66

Find and Interpret the Area under a Normal Curve
A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls followed a normal distribution with an average of $800 per month and a standard deviation of $50 per month. Refer to such expenses as PCE s (personal call expenses). Using the distribution above, what is the probability that a randomly selected month had a PCE of between $675.00 and $890.00

A) 0.9579
B) 0.0421
C) 0.9999
D) 0.0001

Question 67

Find and Interpret the Area under a Normal Curve
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1300 miles. What is the probability a particular tire of this brand will last longer than 58,700 miles

A) 0.8413
B) 0.1587
C) 0.2266
D) 0.7266

Question 68

Find and Interpret the Area under a Normal Curve
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a certain tire of this brand will last between 53,910 miles and 54,780 miles

A) 0.0180
B) 0.9813
C) 0.4920
D) 0.4649

Question 69

Find and Interpret the Area under a Normal Curve
A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $700 per month and a standard deviation of $50 per month. Refer to such expenses as PCE s (personal call expenses). Find the probability that a randomly selected month had a PCE that falls below $550.

A) 0.0013
B) 0.7857
C) 0.2143
D) 0.9987

Question 70

Find and Interpret the Area under a Normal Curve
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.43 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 12.33 ounces of beer.

A) 0.0062
B) 0.4938
C) 0.9938
D) 0.5062

Question 71

Find and Interpret the Area under a Normal Curve

Question 72

Find and Interpret the Area under a Normal Curve
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 3.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 2.5 minutes.

A) 0.3085
B) 0.1915
C) 0.3551
D) 0.2674

Question 73

Find and Interpret the Area under a Normal Curve
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 322 seconds.

A) 0.0107
B) 0.4893
C) 0.9893
D) 0.5107

Question 74

Find and Interpret the Area under a Normal Curve
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 378 seconds to run the mile.

A) 0.9893
B) 0.4893
C) 0.0107
D) 0.5107

Question 75

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%

Question 76

Find and Interpret the Area under a Normal Curve

Question 77

Find and Interpret the Area under a Normal Curve
Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 11.14 onces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more than 11.14 ounces of beer.

A) 0.5
B) 1
C) 0
D) 0.4

Question 78

Find and Interpret the Area under a Normal Curve
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 3.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 2.0 and 4.5 minutes to find a parking spot in the library lot.

Question 79

Find and Interpret the Area under a Normal Curve

Question 80

Find and Interpret the Area under a Normal Curve