1. (a) The time, X minutes, taken by Fred Fast to install a satellite dish may be assumed to be a normal random variable with mean 134 and standard deviation 16.

(i) Determine P(X<150)

(ii) Determine, to one decimal place, the time exceeded by 10 percent of installations.

(b) The time, Y minutes, taken by Sid Slow to install a satellite dish may also be assumed to be a normal random variable, but with

P(Y<170)= 0.14 and P(Y>200)= 0.03

Determine, to the nearest minute, values for the mean and standard deviation of Y.

2. The volume, L litres, of emulsion paint in a plastic tub may be assumed to be normally distributed with mean 10.25 and variance ².

(a) Assuming that ²= 0.04, determine P(L<10).

(b) Find the value of so that 98% of tubs contain more than 10 litres of

emulsion paint.