How to Solve This Math Problem?

An electric car battery is expected to have a life of 60 months with a standard deviation of 12 months. If a sample of 36 batteries is randomly selected, what is the probability that their average lifetime is between 55 and 65 months?

Standard deviation for a sample of 36 = sdev / sqrt(36) = 12 / 6 = 2.

The convert the two targets to Z-scores and look them up on your normal distribution table.

Z = ( value – mean ) / sdev

z1 = ( 55 – 60 ) / 2 = -5 / 2 = -2.5
z2 = ( 65 – 60 ) / 2 = 5 / 2 = +2.5

The table values are .0062 and .9938, so the probability of a value in between =
.9938 – .0062 = .9876 or 98.76%