Deck 6: The Normal Distribution and Other Continuous Distributions

Question 1

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 .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 1

0.3679

Question 2

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?

Answer 2

0.0228

Question 3

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 .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

Answer 3

0.917915

Question 4

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 .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 5

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 6

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 7

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 $\pm$ 1 standard deviation from the mean.
C)It is a discrete probability distribution.
D)Its parameters are the mean,?,and standard deviation,?.

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,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 9

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 10

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 11

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 12

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 .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 13

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

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

Question 14

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 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 die before they reach the standard retirement age of 65?

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 3 minutes .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 17

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 18

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 19

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 20

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 21

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 22

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 23

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

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,above what weight (in pounds)do 89.80% of the weights occur?

Question 25

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

Question 26

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

Question 27

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 28

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 29

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 30

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 31

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

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.Assuming the weights of catfish are normally distributed,the probability that a randomly selected catfish will weigh more than 4.4 pounds is ?

Question 33

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

Question 34

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

Question 35

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 36

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

Question 37

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 38

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 39

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

Question 40

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

Question 41

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 42

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

Question 43

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 44

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 45

The amount of tea leaves in a can from a 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 46

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 47

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 48

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 49

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 50

The amount of tea leaves in a can from a 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 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%.What is the probability that the time elapsed between two consecutive trades will be between 14 and 17 seconds?

Question 52

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 53

The amount of tea leaves in a can from a 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 54

The amount of tea leaves in a can from a 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 55

The amount of tea leaves in a can from a 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 56

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

Question 57

The amount of tea leaves in a can from a 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 58

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 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 less than 124 inches?

Question 60

The amount of tea leaves in a can from a 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 61

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 62

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 63

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 .

Question 64

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 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 lower than 55?

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 between 75 and 90?

Question 67

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 68

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 69

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 70

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 71

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 72

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 73

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 74

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 75

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

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 55 and 90?

Question 78

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 79

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 80

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?