Let X be the lifetime of an electronic device It is known th

Let X be the lifetime of an electronic device. It is known that the average lifetime of the device is 724 days and the standard deviation is 134 days. Let x ¯   be the sample mean of the lifetimes of 213 devices. The distribution of X is unknown, however, the distribution of x ¯   should be approximately normal according to the Central Limit Theorem. Calculate the following probabilities using the normal approximation.

(a) P(x ¯ 715)=

(b) P(x ¯ 733)=

(c) P(712x ¯ 738)=

Solution