Exercises

Exercises for Section  6.1

1.

The national norm of a science test for tenth graders has a mean of 210 and a standard deviation of 28.

(a)

What percentage scored over 220? (You may assume that the histogram of scores looks approximately like the normal curve.)

(b)

One tenth grader is randomly selected. What is the chance that he/she scored over 220?

(c)

A random sample of 40 tenth graders are selected. What is the chance that this group will average over 220? (Should this be smaller, larger, or approximately equal to (b)?)

(d)

A larger sample of 100 tenth graders is selected. What is the probability that this group will average over 220? (Should this be smaller, larger, or approximately equal to (c)?)

2.

The number of customers per week at each store of a supermarket chain has a mean of 4400 and standard deviation 500. Also, 85% of the stores sell lottery tickets.

(a)

What is the probability that a randomly selected store will have less than 4200 customers in a week? (Assume that the number of customers per week is approximately normal.)

(b)

If a random sample of 40 stores is selected, what is the probability that the sample will average below 4200 customers for the week?

(c)

If a random sample of 40 stores is selected, what is the probability that fewer than 75% of the stores sell lottery tickets?

Exercises for Section  6.2

3.

Suppose that healthy human body temperatures average $98.6^{\circ}F$, with a standard deviation of $0.95^{\circ}F$.

(a)

At any one time, what percentage of healthy people have temperatures over $99^{\circ}F$? (You may NOT assume that the histogram of body temperatures looks approximately like the normal curve.)

(b)

25 healthy people are selected at random. What is the probability that their temperatures average $99^{\circ}F$ or higher?

(c)

There is an 80% chance that their temperatures average below _______ $^{\circ}F$.

4.

The time spent per e-mail ``session'' reading and writing personal messages averages 15 minutes, with a standard deviation of 5 minutes.

(a)

What proportion of email sessions last 10 minutes or longer? (You may NOT assume that the histogram of session times looks approximately like the normal curve. It is right skewed.)

(b)

Suppose that 30 e-mail sessions are monitored. What is the probability that the average length will exceed 10 minutes? (Will this probability be the same as (a)?)

(c)

Suppose that 60 e-mail sessions are monitored. What is the probability that the average length will exceed 10 minutes? (Will your answer be smaller, larger, or approximately equal to (b)?)

Exercises for Section  6.3

5.

Safe Skies Airline took a random sample of 25 flights to estimate the average time that arriving passengers wait for luggage at the carousel. The sample average was found to be 16.2 minutes with a standard deviation of 4 minutes. The population average waiting time is estimated as minutes give or take minutes or so.

6.

Brazil was Latin America's leading economic power in the 1970s. In the past, this country has also had one of the highest inflation rates in Latin America. In an attempt to regain investor confidence, the Brazilian government has increased interest rates and has worked to establish a sound fiscal policy to keep inflation under control. Based on a random sample of 60 food items selected in 2001, the inflation rate was estimated as 6% (the sample SD was 1.75%). Find a standard error for this 6% estimate.

7.

A manufacturing company's profits depend on the cost of materials. One material of interest is carbon fiber, which is used to make golf shafts and fishing rods. The cost per pound (in dollars) was recorded for ten randomly selected days from the first six months of 2002. The data follow:

7.6, 7.8, 8.8, 7.3, 6.6, 7.5, 6.7, 8.6, 7.4, 7.7

(a)

Calculate an estimate for the average cost per pound during the first six months of 2000.

(b)

Calculate a standard error for your estimate in (a).

8.

The Federal Reserve board made eight interest-rate cuts on its benchmark short-term rates during 2001. However, credit cards have averaged around 14%, with the lowest credit cards charging around 8%. A financial analyst believes that the average rate on credit cards that charge monthly fees is lower than the national average of all credit cards. A random sample of 29 different credit cards that charged monthly fees revealed a sample mean of 13.2% with a sample standard deviation of 1.4%.

(a)

Calculate an estimate for the average rate of cards that charge monthly fees.

(b)

Calculate a standard error for your estimate in (a).

(c)

Consider the possibility that the true population average rate for cards that charge monthly fees is 14%, and luck-of-the-draw caused the sample to be below average. What is the chance of getting a sample average as low as 13.2% if indeed the population average is 14%?