On average, 8% of the candidates sitting an examination are awarded a merit. Groups of 50 candidates

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On average, 8% of the candidates sitting an examination are awarded a merit. Groups of 50 candidates are selected at random.

a. How many candidates in each group are not expected to be awarded a merit?

b. Calculate the variance of the number of merits in the groups of 50.

c. Find the probability that:

i. Three, four or five candidates in a group of 50 are awarded merits

ii. Three, four or five candidates in both of two groups of 50 are awarded merits.

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