Frugal Bakeries claim that packs of ten of their buns contain on average 75 raisins. A Poisson

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Frugal Bakeries claim that packs of ten of their buns contain on average 75 raisins. A Poisson distribution is used to model the number of raisins in a randomly selected bun.

(a) Specify the value of the parameter.

(b) State any assumption required about the distribution of raisins in the production process for this model to be valid.

(c) Show that the probability that a randomly selected bun contains more than eight raisins is 0.338.

(d) Find the probability that in a pack of ten buns at least two buns contain more than eight raisins.

(e) Using a suitable approximation, find the probability that in a pack of ten buns there are more than 80 raisins. (L)

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