Question

When a computer disk manufacturer tests a disk, it writes to the disk and then tests it using a certifier. The certifier counts the number of missing pulses or errors.

The manufacturer counts an average of 120 errors per 30 test areas. It is assumed that the errors occur individually, independently and at a uniform rate. Let X be the number of errors on a specified test area of interest.

1. Give an expression for the probability that exactly 50 errors occur in 7 areas of interest.
2. Show that the probability that in 1 area, at least 8 but fewer than 11 errors are occur is

0.048. You should calculate it to at least 4 decimal places. Use 0.05 in the rest of this question.

3. The manufacturer is being audited and is asked to track and record the number of errors that occur per area over 30 non-overlapping areas. What is the probability that more than 1 of these areas are found to have at least 8 but fewer than 11 errors occur?

Answer 1

The number of errors in a certain number of test areas X can be modeled by Poisson distribution.

The Poisson PMF is

a) The Poisson parameter for 7 areas is

The probability that exactly 50 errors occur in 7 areas of interest is

b) The Poisson parameter for 1 area is

The probability that in 1 area, at least 8 but fewer than 11 errors are occur is

The proof is complete.

c) Use Binomial distribution with . Let

The probability,