A firms office contains 150 PCs The probability that exactly

A firm\'s office contains 150 PCs. The probability that exactly one computer will not work on a given day is 0.05.

a) On a given day what is the probability that exactly one computer will not be working?

b) On a given day what is the probability that at least two computers will not be working?

c) What assumptions do your answers in (a) and (b) require? Do you think they are reasonable?

d) Determine the mean and standard deviation of the number computers that will not be working on a given day.

e) Use the BINOMDIST function in Excel to find the probability that the number of computers that will not be working on a given day will lie within two standard deviations of the mean?

Solution

These are Binomial probability problems with n = 150 and p = 0.05 ...

a. On a given day what is the probability that exactly one computer will not be working?

P(1) = 150C1 (0.05^1)(1-0.05)^(149) = 0.0036


b. On a given day what is the probability that at least two computers will not be working?

P( X ? 2) = 1 - P(0) - P(1) = 1 - 150C0 (0.05^0)(1-0.05)^(150) - 0.0036

= 0.9959


c. What assumptions do your answers in parts (a) and (b) require? Do you think they are
reasonable? Explain.

Each computer is \"independent\"
There are only 2 possible outcomes (work or not work)
probability of not working is the same for each computer (that is, p = 0.05)
There are a \"fixed\" number of trials (i.e, 150)


d. Determine the mean and standard deviation of the number computers that will not be working
on a given day

mean = np = (150)(0.05) = 7.5000 computers

std dev = ?(npq) = ?[(150)(0.05)(1-0.05)] = 2.6693 computers