In a city, the mean height of married man is 180 cm with a standard deviation of 4 cm, the mean height of married women is 175 cm with a standard deviation of 3 cm. Assume that the choice of partner in marriage is not influenced by height consideration. A couple is selected at random. Showing all details of your workings for the following computations.

(a) Compute the probability that

(i)both of them are taller than 177.5cm;

(4marks)

(ii)the husband is taller by less than 5cm;

(4marks)

(iii)their height difference is less than 5cm.

(4marks)

(b) 7 more married couples are selected from the city. Compute the probability that at least 2 of the selected couples have height differences of more than 5cm.