a. In a given population 25% of the population choose jogging as their leisure activity.

i. Find the probability that out of 20 people selected at random

exactly five people choose jogging as their leisure activity and at most 17 people do no

choose jogging as their leisure activity

(7 marks)

ii. Use a suitable approximation to find the probability that out of 60 people selected at

random 12,13,14 or 15 choose jogging as their leisure activity.

(8 marks)

b.The number of flaws in a glass sheet has a Poisson distribution with a parameter 0.4.

A random sample of 100 glass sheets taken.

i.By using the central limit theorem state the approximation of the mean number of flaws of

the sample

(2 marks)

ii. Find the probability that the mean number of flaws of the sample is between 0.35 and

0.45

(3 marks)