A certain type of battery has a mean shelf life of 2 years w

A certain type of battery has a mean shelf life of 2 years with a standard deviation of 4 months. Assuming a normal distribution,estimate the probability that a battery chosen at random a) will have a shelf life of at least 2.5 years b) will break down during the 3rd year. Note:use time units of months and sketch the corresponding areas under the standard normal curve for both cases.

Solution

mean = 2 years
standard deviation = 0.33 years

a)
will have a shelf life of at least 3 years;
= 2
= 0.33
standardize x to z = (x - ) /
P(x > 3) = P( z > (3-2) / 0.33)
= P(z > 3) = 0.0013
(From Normal probability table)

b)
P(x=3) = cannot be answered as this is a continuous distribution.