A certain type of battery has a mean shelf life of 25 years

A certain type of battery has a mean shelf life of 2.5 years with a standard deviation of 3 months. Assuming a normal distribution, estimate the probability that a battery chosen at random
a) will have a shelf life of at least 3 years;
b) will break down during the 3rd year;
Sketch the corresponding areas under the standard normal curve for both cases.

Solution

X - life of the battery is normal (2.5, 3/12)

BOth converted into years

a) P(X>3)

= P(Z>2.5/0.25) = P(Z>10) = 0.0000

b) P(2<z<3) = P(-2<z<2)

= 0.9554