The amount of time spent by North American adults watching television per day is

ID: 3059482 • Letter: T

Question

The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours.

a. What is the probability that a randomly selected North American adult watches television for more than 7 hours per day?

b. What is the probability that the average time watching television by a random sample of five North American adults is more than 7 hours?

c. What is the probability that, in a random sample of five North American adults, all watch television for more than 7 hours per day?

Because many passengers who make reservations do not show up, airlines often overbook flights (sell more tickets than there are seats). A Boeing 767-400ER holds 245 passengers. If the airline believes the rate of passenger no-shows is 5% and sells 255 tickets, is it likely that it won’t have enough seats and someone will get bumped?

a. Use Normal approximation to determine the binomial probability of at least 246 passengers showing up.

b. Should the airline change the number of tickets it sells for the flight? Explain.

Suppose at your university, some administrators believe that the proportion of students preferring to take classes at night exceeds 0.30. The president is skeptical and so has an assistant take a simple random sample of 200 students. Of these, 66 indicate that they prefer night classes. What is the probability of finding a sample proportion equal to or greater than that found if the president’s skepticism is justified?

ACNielsen is a New York-based corporation and a member of the modern marketing research industry. One of the items that ACNielsen tracks is the expenditure on overthe-counter (OTC) cough medicines. ACNielsen recently indicated that consumers spent $620 million on OTC cough medicines in the United States. The article also indicated that nearly 30 million visits for coughs were made to doctor’s offices in the United States.

a. Determine the average cost of OTC cough medicines per doctor’s office visit based on 30 million purchases.

b. Assuming that the average cost indicated in part a is the true average cost of OTC cough medicines per doctor’s visit and the standard deviation is $10, determine the probability that the average cost for a random selection of 30 individuals will result in an average expenditure of more than $25 in OTC cough medicines.

c. Determine the 90th percentile for the average cost of OTC cough medicines for a sample of 36 individuals, all of whom have visited a doctor’s office for cough symptoms.

A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution

a. What value will be exceeded 10% of the time?

b. What value will be exceeded 85% of the time?

c. Determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.

Explanation / Answer