Homework Answers

. Assume that arrivals occur according to a Poisson process with an average

of seven per hour. What is the probability that exactly two customers arrive in the two-hour period

of time between

(a) 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?

(b) 1:00 P.M. and 2:00 P.M. or between 3:00 P.M. and 4:00 P.M. (two separate one-hour periods

that total two hours)?

In southern California, a growing number of individuals pursuing teaching credentials are choosing paid internships over traditional student teaching programs. A group of eight candidates for

three local teaching positions consisted of five who had enrolled in paid internships and three who

enrolled in traditional student teaching programs. All eight candidates appear to be equally qualified, so three are randomly selected to fill the open positions. Let Y be the number of internship

trained candidates who are hired.

(a) Does Y have a binomial or hypergeometric distribution? Why?

(b) Find the probability that two or more internship trained candidates are hired

(c) What are the mean and standard deviation of Y ?.

Prove that x(1 + x) > (1 + x) In(1 + x) > x

A corporation is sampling without replacement for n = 3 firms to determine the one from which to

purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are

local and two are not local. Let Y denote the number of nonlocal firms among the three selected.

(a) P(Y = 1).

(b) P(Y ≥ 1).

(c) P(Y ≤ 1).

In an assembly-line production of industrial robots, gearbox assemblies can be installed in one

minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty gearboxes are in stock, 2 with improperly drilled holes. Five gearboxes must be selected from the 20 that are available for installation in the next five robots.

(a) Find the probability that all 5 gearboxes will fit properly.

(b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxe