Note: Use R for computations in the following questions and submit your R. Mathematicalnotations or proofs can be written in a word or pdf document.

Problem 1

The time between calls to a plumbing supply business is exponentially distributed with amean time between calls of 15 minutes.

(a) What is the probability that there are no calls within a 30-minute interval?

(b) What is the probability that at least one call arrives within a 10-minute interval?

(c) What is the probability that the rst call arrives within 5 and 10 minutes after opening?

(d) Determine the length of an interval of time such that the probability of at least onecall in the interval is 0.90.

Problem 2

The length of time (in seconds) that a user views a page on a Web site before moving toanother page is a lognormal random variable with parameters = 0:5 and !2= 1

(a) What is the probability that a page is viewed for more than 10 seconds? (3 points)

(b) What is the length of time that 50% of users view the page? (3 points)

(c) What is the mean and standard deviation of the time until a user moves from the

page? (6 points)Use R for computations in the following questions