4(a) State which standard distribution might serve as a model for each of the fo

Question

4(a) State which standard distribution might serve as a model for each of the following. The number of meteorites above a certain size hitting a particular (2 marks) (i) area of the Earth in a year (ii) The number of items in a batch of fixed size which are faulty (2 marks) iii) The length of time unil the next meteorite above a certain size hits (2 marks) a particular area of the Earth (b) In (a) parts (i) andi, under what circumstances might a Normal approx- imation to the distribution you suggested be appropriate?(4 marks)

Explanation / Answer

(a)

(i) poisson distribution

(ii) binomial distribution

(iii) exponential distribution

b)

in pat (i) expected number of metorites hit in a year should be greater than 15

and in part (ii) if p is probability of faulty item and batch size is n ; then np>=10 and n(1-p)>=10

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