Exercises

Exercises for Section  5.1

1.

According to Horseman's Quarterly, three out of five racehorses lose money. A racing partnership has 49 horses in its stables. What is the probability that more than two-thirds of the stable's horses will lose money?

2.

Suppose that 20% of students in a large university are graduate students. If a random sample of 125 students are randomly selected, What is the probability that 25% or more of the sample are graduate students?

3.

An opinion poll of 800 residents of a large suburb asked whether they favor a rise in taxes to help pay for a new shopping mall. If 60% or more support the tax, a referendum will be placed on the next election ballot. If the true (population) proportion of all residents who favor the mall tax is 55%, what is the probability that a referendum will be placed on the next ballot? (In other words, what is the probability that the sample proportion will reach or exceed 60%?)

4.

Eighty percent of small retail businesses experience cash flow problems during their first year of operation. A consultant takes a random sample of 60 small businesses that have been in business for one year.

(a)

What is the probability that 85% or more of the sampled businesses have experienced cash flow problems?

(b)

What is the probability that less than 70% of the sampled businesses have experienced cash flow problems?

5.

Historically, 92% of the overnight deliveries of a parcel service arrive the next morning before noon (considered ``on time'' delivery). Suppose 300 deliveries are randomly selected for the purposes of quality control.

(a)

What is the probability that more than 90% of the deliveries were on time?

(b)

What is the probability that less than 85% of the deliveries were on time?

Exercises for Section  5.2

6.

A random sample of 200 adult Texas residents is taken, and they were asked whether they approve of the death penalty. Suppose that 80 out of the 200 say they favor the death penalty.

(a)

What is estimate of the proportion of adult Texans who favor the death penalty?

(b)

Calculate a standard error for your estimate.

7.

A recent poll of 400 Kalamazoo residents resulted in a 60% approval rating for President Bush. Calculate a standard error for this estimate.

8.

A sample of 100 individuals showed that 20% experienced gastrointestinal problems after consuming 10 grams of sorbitol, a common artificial sweetener. Attach a standard error to this estimate.