Question

1. Within a computer program, the number of bugs (i.e., coding errors) per lines of code has a Poisson distribution with an average of fifteen bugs per 1,000 lines.

a. Find the probability that there will be exactly eight bugs in 1,000 lines of code.

b. Find the probability that there will be at least eight bugs in 1,000 lines of code.

c. Find the probability that there will be at least one bug in 1,000 lines of code.

d. Find the probability that there will be no more than one bug in 1,000 lines of code.

2. There are ten computers in a PC lab. The probability that any of the computers is used at any given moment is 15%. Answer the following:

a. What is the probability that exactly three computers are being used?

b. What is the probability that more than five computers are being used?

c. What is the probability that less than five computers are being used?

d. What is the probability that a group of three students would be able to work together in the PC lab assuming they each need a computer?

e. What is the expected number of computers being used at any given moment? What does this number mean?

Answer 1

1)

poisson probability distribution

P(X=x) = e-λλx/x!

Mean/Expected number of events of interest: λ =                15 bugs per 1000 lines

a) P ( X =    8   ) = e^-15*15^8/8!=   0.0194

b) P(X≥8) = Σe^-λλ^x/x! where x varies from 8 to 15 = 0.9820

c) P ( X =    0   ) = e^-15*15^0/0!=   0.0000

P(at least 1) = 1 - P(x=0) = 0.99999969410

d) P(X≤1) = P(X=0) + P(X=1) = 0.000004894