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.
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.
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