Question

(a) An office has a stock of identical printed forms which are used independently. On
any working day, at most one of the forms is used, and the probability that one
form is used is 1/3. There are 250 working days in the year.

(i) Using a suitable approximation, calculate the number of forms that must be
in stock at the beginning of the year if there is to be a 95% probability that
they will not all be used before the end of the year. [5 marks]

(ii) If one form in one hundred is unusable due to faulty printing and these faults
occur at random, calculate the probability that in a batch of 250 forms there
will be not more than one which is unusable. [3 marks]

Answer 1

The number of forms used in 250 days has exact distribution .

i)The normal approximation is

Let be the number of forms in stock at the beginning of the year if there is to be a 95% probability that
they will not all be used before the end of the year. Then

ii) The number of unusable forms out of 250 forms has Poisson distribution.

The Poisson PMF is

.

The Poisson parameter for 250 forms is  .

The required probability is