Question 1:

Suppose a geyser has a mean time between eruptions of 84 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 33 minutes, answer the following questions.

(a) The probability that a randomly selected time interval is longer than 100 minutes is approximately

(b) What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 100 minutes?

(c) What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 100 minutes?

Question 2:

The average salary for a certain profession is 584,500. Assume that the standard deviation of such salaries is $33.000. Consider a random sample of 55 people in this profession and let x represent the mean salary for the sample.

A The shape is that of a uniform distribution.

B. The shape is that of a binomial distribution.

c. The shape is that of a poisson distribution.

D.The shape is that of a normal distribution.

Question 3:

The time required for an automotive center to complete an change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes and a standard deviation of 3.5 minutes.

(a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price?

(b) If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit?

(c) The percent of customers that receive the service for half-price is 12.661%. (Round to two decimal places as needed.)

(d) The guaranteed time limit is EN minutes. (Round up to the nearest minute.)