In each of the following three situations, use the binomial, poisson, or normal
distribution depending on which is the most appropriate.
In each case, explain why you selected the distribution and draw attention to any
feature which supports or casts doubt on the choice of distribution.

(a) Situation 1:
The lifetimes of a certain type of electrical components are distributed with a
mean of 800 hours and standard deviation of 160 hours.
Required:
(i) Identify situation 1. (2 marks)
(ii) If the manufacturer replaces all components that fail before the
guaranteed minimum life time of 600 hours, what percentage of the
components have to be replaced?
(3 marks)
(iii) If the manufacturer wishes to replace only 1% of the components that
have the shortest life, what value should be used as the guaranteed
lifetime? (3 marks)
(iv) What is the probability that the mean lifetime of a sample of 25 of these
electrical components exceeds 850 hours? (2
marks)

(b) Situation 2:
A green grocer buys peaches in large consignments directly from a wholesaler.
In view of the perishable nature of the commodity, the green grocer accepts
that 15% of the supplied peaches will usually be unsalable. As he cannot check
all the peaches individually, he selects a single batch of 10 peaches on which to
base his decision of whether to purchase a large consignment or not. If no
more than two of these peaches are unsatisfactory, the green grocer purchases
the consignment.
Required:
(i) Identify situation 2 (2 marks)
(ii) Determine the probability that under normal supply conditions, the
consignment is purchased. (3 marks)
(c) Situation 3
Vehicles pass a certain point on a busy single – lane road at an average rate of
two per 10 second interval.
Required:
(i) Identify situation (3) (2 marks)
(ii) Determine the probability that more than three cars pass this point
during a 20
second interval. (3 marks)