Deck 6: The Normal Distribution and Other Continuous Distributions

Question 1

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.Find the age at which payments have ceased for approximately 86% of the plan participants.

Answer 1

71.78 years old

Question 2

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes (i.e.the mean number of calls answered in a minute is ).What proportion of callers is put on hold longer than 2.8 minutes?

A)0.3679
B)0.50
C)0.60810
D)0.6321

Answer 2

A

Question 3

If we know that the length of time it takes a college student 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 and 4.5 minutes to find a parking spot in the library parking lot.

A)0.0919
B)0.2255
C)0.4938
D)0.7745

Answer 3

D

Question 4

If we know that the length of time it takes a college student 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 find a parking spot in the library parking lot in less than 3 minutes.

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

Question 5

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes (i.e.the mean number of calls answered in a minute is ).What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

A)0.86466
B)0.60653
C)0.39347
D)0.13534

Question 6

The value of the cumulative standardized normal distribution at 1.5X is 0.9332.The value of X is

A)0.10.
B)0.50.
C)1.00.
D)1.50.

Question 7

The value of the cumulative standardized normal distribution at Z is 0.8770.The value of Z is

A)0.18.
B)0.81.
C)1.16.
D)1.47.

Question 8

If we know that the length of time it takes a college student 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,75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?

A)2.8 minutes
B)3.2 minutes
C)3.4 minutes
D)4.2 minutes

Question 9

If a particular set of data is approximately normally distributed,we would find that approximately

A)2 of every 3 observations would fall between ±1 standard deviation around the mean.
B)4 of every 5 observations would fall between ±1.28 standard deviations around the mean.
C)19 of every 20 observations would fall between ±2 standard deviations around the mean.
D)All of the above.

Question 10

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes (i.e.the mean number of calls answered in a minute is ).Find the waiting time at which only 10% of the customers will continue to hold.

A)2.3 minutes
B)3.3 minutes
C)6.9 minutes
D)13.8 minutes

Question 11

For some value of Z,the value of the cumulative standardized normal distribution is 0.2090.The value of Z is

A)-0.81.
B)-0.31.
C)0.31.
D)1.96.

Question 12

Which of the following about the normal distribution is not true?

A)Theoretically,the mean,median,and mode are the same.
B)About of the observations fall within ±1 standard deviation from the mean.
C)It is a discrete probability distribution.
D)Its parameters are the mean,μ and standard deviation,σ.

Question 13

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.What proportion of the plan recipients would receive payments beyond age 75?

Question 14

For some value of Z,the value of the cumulative standardized normal distribution is 0.8340.The value of Z is

A)0.07.
B)0.37.
C)0.97.
D)1.06.

Question 15

In its standardized form,the normal distribution

A)has a mean of 0 and a standard deviation of 1.
B)has a mean of 1 and a variance of 0.
C)has an area equal to 0.5.
D)cannot be used to approximate discrete probability distributions.

Question 16

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes (i.e.the mean number of calls answered in a minute is ).What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?

A)0.0009119
B)0.082085
C)0.917915
D)0.9990881

Question 17

The value of the cumulative standardized normal distribution at Z is 0.6255.The value of Z is

A)0.99.
B)0.40.
C)0.32.
D)0.16.

Question 18

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.What proportion of the plan recipients die before they reach the standard retirement age of 65?

Question 19

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2,find the probability that X is between 47 and 54.

Question 20

A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes (i.e.the mean number of calls answered in a minute is ).What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order?

A)0.22313
B)0.48658
C)0.51342
D)0.77687

Question 21

A quality control manager at a plant that produces o-rings is concerned about whether the diameter of the o-rings that are produced is conformable to the specification.She has calculated that the average diameter of the o-rings is 4.2 centimeters.She also knows that approximately 95% of the o-rings have diameters that fall between 3.2 and 5.2 centimeters and almost all of the o-rings have diameters between 2.7 and 5.7 centimeters.When modeling the diameters of the o-rings,which distribution should the scientists use?

A)Uniform distribution
B)Binomial distribution
C)Normal distribution
D)Exponential distribution

Question 22

A food processor packages orange juice in small jars.The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce.Find the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces.

Question 23

It was believed that the probability of being hit by lightning is the same during the course of a thunderstorm.Which of the following distributions would you use to determine the probability of being hit by lightning during the first half of a thunderstorm?

A)Normal distribution
B)Poisson distribution
C)Uniform distribution
D)Exponential distribution

Question 24

A wheel spinning game is played with a special wheel with 24 equal segments that determine the dollar values of a single spin.Which of the following distributions can best be used to compute the probability of winning a specific dollar value in a single spin?

A)Uniform distribution
B)Binomial distribution
C)Normal distribution
D)Exponential distribution

Question 25

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.A citation catfish should be one of the top 2% in weight.Assuming the weights of catfish are normally distributed,at what weight (in pounds)should the citation designation be established?

A)1.56 pounds
B)4.84 pounds
C)5.20 pounds
D)7.36 pounds

Question 26

Let X represent the amount of time till the next student will arrive in the library parking lot at the university.If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes (i.e.the mean number of arrivals is per minute),find the probability that it will take between 2 and 12 minutes for the next student to arrive at the library parking lot.

A)0.049787
B)0.556744
C)0.606531
D)0.656318

Question 27

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed,the probability that a randomly selected catfish will weigh less than 2.2 pounds is ________.

Question 28

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes.Which of the following distributions would you use to determine the probability that a defective light bulb will be produced in a 15-minute interval?

A)Normal distribution
B)Poisson distribution
C)Uniform distribution
D)Exponential distribution

Question 29

The amount of juice that can be squeezed from a randomly selected orange out of a box of oranges with approximately the same size can most likely be modeled by which of the following distributions?

A)Uniform distribution
B)Poisson distribution
C)Normal distribution
D)Exponential distribution

Question 30

A food processor packages orange juice in small jars.The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce.Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.

Question 31

Suppose the light bulbs in a factory burn out at a rate of 50 bulbs per month.Which of the following distributions would you use to determine the probability that the next two light bulbs will burn out 2 days apart?

A)Hypergeometric distribution
B)Poisson distribution
C)Uniform distribution
D)Exponential distribution

Question 32

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed,above what weight (in pounds)do 89.80% of the weights occur?

Question 33

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed,the probability that a randomly selected catfish will weigh between 3 and 5 pounds is ________.

Question 34

Let X represent the amount of time until the next student will arrive in the library parking lot at the university.If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes (i.e.the mean number of arrivals is per minute),find the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot.

A)0.917915
B)0.670320
C)0.329680
D)0.082085

Question 35

The Tampa International Airport (TIA)has been criticized for the waiting times associated with departing flights.While the critics acknowledge that many flights have little or no waiting times,their complaints deal more specifically with the longer waits attributed to some flights.The critics are interested in showing,mathematically,exactly what the problems are.Which type of distribution would best model the waiting times of the departing flights at TIA?

A)Uniform distribution
B)Binomial distribution
C)Normal distribution
D)Exponential distribution

Question 36

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

A)Uniform distribution
B)Poisson distribution
C)Normal distribution
D)Exponential distribution

Question 37

Suppose students arrive at an advising office at a rate of 30 per hour.Which of the following distributions would you use to determine the probability that the next two students will arrive 30 minutes apart?

A)Normal distribution
B)Poisson distribution
C)Uniform distribution
D)Exponential distribution

Question 38

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed,the probability that a randomly selected catfish will weigh more than 4.4 pounds is ________.

Question 39

Suppose the probability of finding a defective spot in an area on a piece of glass is the ratio of that area to the total area of the glass and the probability is the same across the whole glass.Which of the following distributions would you use to determine the probability of finding a defective spot in a randomly selected one square inch area on a piece of 10 feet by 10 feet glass?

A)Normal distribution
B)Poisson distribution
C)Uniform distribution
D)Exponential distribution

Question 40

Suppose the probability of a car accident taking place anywhere on a 20-mile stretch of highway is the same.Which of the following distributions would you use to determine the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?

A)Normal distribution
B)Poisson distribution
C)Uniform distribution
D)Exponential distribution

Question 41

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected can will contain less than 100 grams or more than 120 grams of tea leaves?

Question 42

True or False: Theoretically,the mean,median,and the mode are all equal for a normal distribution.

Question 43

True or False: The probability that a standard normal variable,Z,falls between -1.50 and 0.81 is 0.7242.

Question 44

True or False: The probability that a standard normal variable,Z,is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

Question 45

The probability that a standard normal variable Z is positive is ________.

Question 46

True or False: The probability that a standard normal variable,Z,falls between -2.00 and -0.44 is 0.6472.

Question 47

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected can will contain between 82 and 100 grams of tea leaves?

Question 48

True or False: The probability that a standard normal variable,Z,is less than 5.0 is approximately 0.

Question 49

True or False: A normal probability plot may be used to assess the assumption of normality for a particular set of data.

Question 50

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

Question 51

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected can will contain between 100 and 110 grams of tea leaves?

Question 52

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected can will contain between 100 and 120 grams of tea leaves?

Question 53

True or False: The probability that a standard normal variable,Z,is between 1.00 and 3.00 is 0.1574.

Question 54

True or False: The probability that a standard normal variable,Z,is below 1.96 is 0.4750.

Question 55

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.Approximately 83% of the can will have at least how many grams of tea leaves?

Question 56

True or False: The "middle spread," that is the middle 50% of the normal distribution,is equal to one standard deviation.

Question 57

True or False: Any set of normally distributed data can be transformed to its standardized form.

Question 58

True or False: A worker earns $15 per hour at a plant in China and is told that only 2.5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,the average wage for the plant is $7.50 per hour.

Question 59

True or False: If a data set is approximately normally distributed,its normal probability plot would be S-shaped.

Question 60

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected can will contain less than 100 grams of tea leaves?

Question 61

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed between two consecutive trades will be between 14 and 17 seconds?

Question 62

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score lower than 55?

Question 63

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.The probability is 20% that the time lapsed will be shorter than how many seconds?

Question 64

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed between two consecutive trades will be longer than 17 seconds?

Question 65

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed between two consecutive trades will be between 13 and 16 seconds?

Question 66

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed between two consecutive trades will be between 15 and 16 seconds?

Question 67

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 55 and 90?

Question 68

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.What proportion of the boards will be less than 124 inches?

Question 69

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.The middle 60% of the time lapsed will fall between which two numbers?

Question 70

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score greater than 95?

Question 71

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 60 and 95?

Question 72

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed between two consecutive trades will be between 13 and 14 seconds?

Question 73

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed between two consecutive trades will be between 14 and 15 seconds?

Question 74

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 90 and 95?

Question 75

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.What proportion of the boards will be over 125 inches in length?

Question 76

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.What proportion of the boards will be between 121 and 124 inches?

Question 77

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 60 and 75?

Question 78

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 75 and 90?

Question 79

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.The probability is 80% that the time lapsed will be longer than how many seconds?

Question 80

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.The middle 86% of the time lapsed will fall between which two numbers?