A high-volume printer produces minor print-quality errors on a test pattern of 1000 pages of text according to a Poisson distribution with a mean of 0.4 per page.

(a) Why are the numbers of errors on each page independent random variables?

(b) What is the mean number of pages with errors (one or more)?

(c) Approximate the probability that more than 350 pages contain errors (one or more).

Step 1 of 5:

Let X follows the Poisson distribution with the probability density function

P(X = x) =

Where, = 10,000.

The claim is to find the probability of more than 20,000 hits in a day.Then, P(X 20000.5) = P(Z )

= P(Z 100.005)

= 0 ( from the area under normal curve table)

Hence, the probability of more than 20,000 hits in a day is 0.

Step 2 of 5:

b) the claim is to find the probability of less than 9900 hits in a day.

Then, P(X < 9899.5) = P(Z )

= P(Z -1.01)

= 0.1562. ( from the area under normal curve table)

Hence, the probability of less than 9900 hits in a day is 0.1562.

Step 3 of 5:

c) the claim is to find the probability that the number of hits in a day exceeds the value is 0.01

Then, P(X > x) = 0.01

=

= 2.33

(x + 0.5) - 10000 = 233

x = 10232.5

Hence, x = 10232.5.