4.1 List the conditions a discrete random variable must satisfy so that it can describe by the binomial distribution. (4 marks)

4.2 Statistics show that 4 in 10 South African adult males have regular medical check-ups. If 10 South African adult males were selected randomly, calculate the probability that:

4.2.1 exactly two have regular medical check-ups. (3 marks)

4.2.2 two or more have regular check-ups. (5 marks)

4.3 The service time for the first service of a certain make of car is found to be normally distributed with a mean of 70 min and a variance of 81 min2.

4.3.1 What percentage of first service will be completed 50 to 60 minutes?

4.3.2 The dealership has policy of giving its customers a 15% discount if the service is not completed within 80 minutes.. From a sample of 80 customers who brought their cars in for first service, how many are likely to receive the discount?