According to a survey, high school girls average 100 text messages daily. Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken.

1. What is the probability that the sample mean is more than 105?
2. What is the probability that the sample mean is less than 95?
3. What is the probability that the sample mean is between 95 and 105?

The weight of people in a small town in Missouri is known to be normally distributed with a mean of 180 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3,200 pounds or 16 persons." What is the probability that a random sample of 16 persons will exceed the weight limit of 3,200 pounds?

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 33.8 and 3.5 mpg, respectively.

1. What is the probability that a randomly selected passenger car gets more than 35 mpg?
2. What is the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg?
3. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 35 mpg?

Suppose that a study finds that 33% of teenagers text while driving. The study was based on 100 teen drivers.

1. Discuss the sampling distribution of the sample proportion.
2. What is the probability that the sample proportion is less than 0.30?
3. What is the probability that the sample proportion is within0.02 of the population proportion?

A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 40 customers. The dealer will be fined if the number of customers who report favorably is between 22 and 26. The dealership will be dissolved if fewer than 22 customers report favorably. It is known that 70% of the dealer's customers report favorably on satisfaction surveys.

1. What is the probability that the dealer will be fined?
2. What is the probability that the dealership will be dissolved?