The mean number of accidents in a shoe factory is 0.10 per day. Suppose you were

Question

The mean number of accidents in a shoe factory is 0.10 per day. Suppose you were asked to find the probability that during a randomly selected day there will be no accidents:

(a) (i)   which distribution does this scenario fit and why?                            (2 marks)

      (ii) define the variable of interest, X.                                                        (1 mark)

      (iii) what are the possible values of X?                                                      (1 mark)

(b)       What is the probability that there will be more than one accident? (3 marks)

Explanation / Answer

a) i) This is Poisson distribution. Because each accident is independent to each other.

ii) X = number of accidents per day in the shoe factory

iii) X can take any positive integer value starting from 0 i.e. 0, 1, 2, 3, ...

b) P(X > 1) = 1 - (P(X = 0) + P(X = 1))

                  = 1 - (e-0.1 * 0.10 / 0! + e-0.1 * 0.11 / 1!)

                  = 1 - 0.9953

                  = 0.0047

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