Deck 6: The Normal Distributions and Other Continuous Distributions

Question 1

If a 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 the above.

Answer 1

All the above.

Question 2

A company that receives most 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 1/3).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

Answer 2

6.9 minutes

Question 3

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

Answer 3

- 0.81

Question 4

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 5

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 6

A company that receives most 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 1/2.8).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 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

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 9

A company that receives most 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 1/3).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 10

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.

Question 11

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 12

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

A)Theoretically, the mean, median, and mode are the same.
B)About 2/3 of the observations fall within standard deviation from the mean.
C)It is a discrete probability distribution.
D)Its parameters are the mean, , and standard deviation,

Question 13

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

Question 14

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 15

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 16

A company that receives most 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 1/2.8).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

Question 17

A company that receives most 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 1/3).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 18

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 19

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 20

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 21

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

Question 22

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 1/4 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 23

A normal probability plot may be used to assess the assumption of normality for a set of data.

Question 24

The owner of a fish market determined that the mean 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 25

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

Question 26

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 27

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

Question 28

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

Question 29

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 30

Any set of normally distributed data can be transformed to its standardized form.

Question 31

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 mean wage for the plant is $7.50 per hour.

Question 32

The owner of a fish market determined that the mean 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 33

The owner of a fish market determined that the mean 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 34

Theoretically, the mean, median, and the mode are all equal for a normal distribution.

Question 35

The probability that a standard normal variable, Z, is below 1.96 is 0.4750.

Question 36

The owner of a fish market determined that the mean 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 37

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 1/4 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 38

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 39

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

Question 40

The owner of a fish market determined that the mean 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 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

The amount of tea leaves in a can from a production line is normally distributed with = 110 grams and = 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 48

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 49

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

Question 50

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

Question 51

You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%.The probability is 20% that the time elapsed will be shorter how many seconds?

Question 52

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

Question 53

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

Question 54

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 55

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

Question 56

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

Question 57

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

Question 58

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

Question 59

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 60

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

Question 61

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.33 and 2.33 is __________.

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 between 60 and 75?

Question 63

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%.The middle 95.46% of the students will score between which two scores?

Question 64

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.89 and -1.03 is __________.

Question 65

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 66

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 67

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z values are larger than __________ is 0.3483.

Question 68

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 69

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -0.88 and 2.29 is __________.

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%.The middle 86.64% of the students will score between which two scores?

Question 71

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is __________.

Question 72

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than 0.77 is __________.

Question 73

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 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 75 and 90?

Question 75

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

Question 76

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 95?

Question 77

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

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 greater than 95?

Question 79

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than -2.20 is __________.

Question 80

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than -0.98 is __________.