Deck 6: The Normal Distribution

Question 1

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 ?

Answer 1

0.1056

Question 2

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

Answer 2

1.00

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

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 5

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 6

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 7

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 inthe library parking lot in less than 3 minutes.

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

Question 8

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 9

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 10

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 11

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 12

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 13

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 14

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 finda parking spot in the library parking lot?

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

Question 15

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 16

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 standarddeviation of 3.5 years.Find the age at which payments have ceased for approximately 86% of the plan participants.

Question 17

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, $\mu$ , and standard deviation, $\sigma$ .

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 standarddeviation of 3.5 years.What proportion of the plan recipients would receive payments beyond age75?

Question 19

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 20

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 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 below10.875 ounces.

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

The probability that a standard normal variable, Z, falls between - 1.50 and 0.81 is0.7242.

Question 27

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

Question 28

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

Question 29

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

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 above10.95 ounces.

Question 31

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

Question 32

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

Question 33

The probability that a standard normal variable, Z, is between 1.00 and 3.00 is0.1574.

Question 34

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

Question 35

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 36

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

Question 37

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

Question 38

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

Question 39

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 40

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

Question 41

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 than95?

Question 42

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

Question 43

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 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%.The probability is 80% that the time elapsed will be longer than how many seconds?

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%.The middle 86% of the time elapsed will fall between which two numbers?

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%.What is the probability that the time elapsed between two consecutive trades will be between 14 and 17 seconds?

Question 47

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 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 13 and 14 seconds?

Question 49

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 and75?

Question 50

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 over125 inches in length?

Question 51

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 and90?

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%.What is the probability that the time elapsed between two consecutive trades will be between 15 and 16 seconds?

Question 53

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 and95?

Question 54

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 55

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 56

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

Question 57

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 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%.The middle 60% of the time elapsed will fall between which two numbers?

Question 59

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 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%.What is the probability that the time elapsed between two consecutive trades will be between 14 and 15 seconds?

Question 61

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,50% of the possible Z values are between and (symmetrically distributed about the mean).

Question 62

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,85% of the possible Z values are smaller than .

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%.What is the probability of a score between 55 and90?

Question 64

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 65

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 66

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 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 and95?

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

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 -2.33 and 2.33 is .

Question 70

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 71

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 0.6985.

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

Question 73

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 74

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability isthat a product is assembled in between 14 and 16 minutes.

Question 75

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 and95?

Question 76

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability isthat a product is assembled in less than 12 minutes.

Question 77

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,96% of the possible Z values are between and (symmetrically distributed about the mean).

Question 78

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 79

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,27% of the possible Z values are smaller than .

Question 80

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 _.