# STATS Problem 1: A consumer advocate claims that 80 percent of cable television

Question

Problem 1: A consumer advocate claims that 80 percent of cable television subscribers are not satisfied with

their cable service. In an attempt to justify this claim, a randomly selected sample of 50 cable subscribers is

selected. Assuming independence, find:

1) The probability that 30 or fewer subscribers in the sample are not satisfied with their service.

2) The probability the more than 40 subscribers in the sample are not satisfied with their service.

3) The probability that between 40 and 45 (inclusive) subscribers in the sample are not satisfied with

their service.

4) The probability that exactly 25 subscribers in the sample are satisfied with their service.

5) Suppose that when we survey 50 randomly selected cable television subscribers, we find that 30 are

not satisfied with their service. Using a probability you found in this problem as the basis for you

answer, do you believe the consumer advocate’s claim? Explain in one or two sentences.

Problem 2: A consensus forecast is the average of a large number of individual analysts’ forecasts. Suppose the

individual forecasts for a particular interest rate are normally distributed with a mean of 5.0 percent and

standard deviation of 1.2 percent. A single analyst is randomly selected.

a. Find the probability that his/her forecast is:

1) At least 3.5 percent.

2) At most 6 percent.

3) Between 3.5 and 6 percent.

b. What percentage of individual forecasts are at or below the 10th percentile of the distribution of

forecasts? What percentage are at or above the 10th percentile? Find the 10th percentile of the

distribution of individual forecasts.

c. Find the first quartile, Q1 and the third quartile, Q3, of the distribution of individual forecasts.

Problem 3: Each day a manufacturing plant receives a large shipment of drums of Chemical ZX-900. These

drums are supposed to have a mean fill of 50 gallons, while the fills have a standard deviation known to be 0.6

gallons.

a. Suppose that mean fill for the shipment is actually 50 gallons. If we draw a random sample of 100

drums from the shipment, what is the probability that the average fill for the 100 drums is between 49.88

gallons and 50.12 gallons?

b. The plant manager is worried that the drums of Chemical ZX-900 are undefiled. Because of this, she

decides to draw a sample of 100 drums from each daily shipment and will reject the shipment (send it

back to the supplier) if the average fill for the 100 drums is less than 49.85 gallons. Suppose that a

shipment that actually has a mean fill of 50 gallons is received. What is the probability that this

shipment will be rejected and sent back to the supplier? What percent of the time will this happen?

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