A transistor radio operates on two 1 volt batteries, so that nominally it operates on 3 volts. Suppose the actual voltage of a single

A transistor radio operates on two 1 ½ volt batteries, so that nominally it operates on 3 volts. Suppose the actual voltage of a single new battery is normally distributed with mean 1 ½ volts and variance 0.0625. The radio will not operate “properly” at the outset if the voltage falls outside the range 23 4 to 31 4 volts.
(a) What is the probability that the radio will not operate “properly”?
(b) Suppose that the assumption of normality is not valid. Give a bound on the probability that the radio will not operate “properly.”