(3 Random sultanas in scones (a) Show that for a Poisson distribution the mean is equal to the variance. (b) In a bakery 3600 sultanas are added to a mixture which is subsequently divided up to make 1200 fruit scones. Assuming that the number of sultanas in each scone follows a Poisson distribution, estimate (i) the number of scones which will be without a sultana; (ii) the number with 5 or more sultanas.

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