Question

3) The amount of time it takes for a grocery clerk to check out a customer is evenly distributed between 1 and 5 minutes.

a. What kind of distribution is this?

b. What is the probability that it will take more than 4 minutes to check out the customer?

c. What is the probability that it will take between 2 and 4 minutes?

d. What is the probability that it will take exactly 2 minutes?

4) A bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in less than 10 minutes. A management scientist has studied the service times and concluded that service times are exponentially distributed with a mean of 5 minutes. Determine what the bank means when it claims virtually all its customers are served in under 10 minutes

6) For the following problems, identify the hypotheses, define Type I and Type II errors, and discuss the consequences of each error. (When you set up the hypotheses, consider which is the hypothesis you are ”trying to prove”, and that is your alternative. The null hypothesis is then the status quo.)

a. The FDA judges the safety of new drugs. When faced with a new drug, there are two possible decisions: approve the drug or disapprove the drug.

b. You are faced with two investments. One is very risky, but potential returns are high, while the other one is safe but the potential is quite limited. Pick one.

c. You are an airline pilot. You smell smoke in the cockpit, and the nearest airport is less than 5 minutes away. Should you land the plane immediately?

7) I am shopping for a dresser on KSL. I look at 30 dressers. I know the standard deviation of dresser prices is $20, and the mean cost of the dressers I look at is $80. I had been told that dressers should be $50.

(a) Write down the null and alternative hypotheses.

(b) What is the value of the test statistic?

(c) What is the p-value? Interpret this value.

(d) What is the rejection region if α = .04?

(e) Interpret the result - do we accept or reject the null hypothesis.

(f) Create a 95% confidence interval for the true average cost of a dresser and interpret the confidence interval.

Answer 1

3) The amount of time it takes for a grocery clerk to check out a customer is evenly distributed between 1 and 5 minutes.

Let X is a random variable shows the amount of time it takes for a grocery clerk to check out a customer.

a. What kind of distribution is this?

Here X has uniform distribution between 1 and 5 so pdf will be

b. What is the probability that it will take more than 4 minutes to check out the customer?

The probability that it will take more than 4 minutes to check out the customer is

c. What is the probability that it will take between 2 and 4 minutes?

d. What is the probability that it will take exactly 2 minutes?

Since it is continuous distribution so probability at a specific point will be zero.That is

P(X=2) = 0