Week 6: Quiz 6

Question 1

In its standardized form, the normal distribution:

• a. Has a mean of 1 and a standard deviation of 1

• b. Has a mean of 0 and a variance of 1

• c. Has an area under the curve equal to 0.5

Question 2

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

• a. 1.47

• b. 0.18

• c. 1.16

Question 3

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 are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is:

• a. 0.0668

• b. 0.5865

• c. 0.1056

Question 4

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

• a. 0.8500

• b. 0.9104

• c. 0.0324

Question 5

A company that sells annuities must base annual payouts on the probability distribution of the length of life of participants. Suppose lifetimes are approximately normally distributed with a mean of 68 years and a standard deviation of 3.5 years. What proportion of participants would receive payments beyond age 75?

• a. 0.0228

• b. 0.0345

• c. 0.0560

Question 6

Using the same scenario as Question 5, find the age at which payments have ceased for approximately 86% of the plan participants:

• a. 69.98

• b. 70.08

• c. 71.78

Question 7

The scores on the final exam for statistics are normally distributed with a mean of 78 and a standard deviation of 10. The highest 55% of scores will pass. What exam score do you need to pass? (Round to nearest integer)

• a. 66

• b. 71

• c. 77

Question 8

The scores on the final exam for Advanced Chemistry are normally distributed with a mean of 78 and a standard deviation of 10. The top 4% of scores receive an “A+”. What score do you need to get an “A”? (Round to nearest integer)

• a. 90

• b. 96

• c. 99

Question 9

Which of the following describes the distinguishing properties of a normal distribution?

• a. Its middle 50% is within 1.33 standard deviations of its mean

• b. Its measures of central tendency are all equal

• c. 99.7% of its values are contained within three standard deviations of its mean

• d. All of the above

Question 10

How can you use the normal probability plot to evaluate whether a set of data is normally distributed?

• a. If normal, the plot of Z values on the horizontal axis and original values on the vertical axis will be a bell curve

• b. If normal, the plot of Z values on the horizontal axis and original values on the vertical axis will be a straight line

• c. If normal, the plot of the standard deviation on the horizontal axis and original values on the vertical axis will be a straight line

• Tutorial for Quiz 6