Batteries for a transistor radio have a mean life under normal usage of 160 hours, with a standard deviation of 30 hours. Assuming the battery life follows a normal distribution,

(a) calculate the percentage of batteries which have a life between 150 hours and 180 hours, (C)

(b) calculate the range, symmetrical about the mean, within which 75% of the battery lives lie. If a radio takes four of these batteries and requires all of them to be working, calculate

(c) the probability that the radio will run for at least 135 hours. (OC)