(a) The lifetime in hours of an electrical component has a normal distribution with mean 150 hours and standard deviation 8 hours. Find the probability that (i) a new component lasts at least 160 hours, (ii) a component which has already operated for 145 hours will last at least another 15 hours.

(b) The weight of these components is normally distributed with mean 250 g and standard deviation 10 g. Each component is in its own box, the weight of which is also normally distributed with mean 50 g and standard deviation 5 g. There are 10 boxed components to a carton and the weight of the carton is normally distributed with mean 75 g and standard deviation 7 g. Find the probability that a carton of 10 boxed components weighs less than 3 kg. (L)