Answer to Question #264430 in Statistics and Probability for Angelo

Question

A certain type of storage battery lasts on average, 3.0 years with a standard deviation of 0.5 year. Assuming the battery life is normally distributed, find the probability that a given battery will last more than 2 years.

Answer 1

$\mu=3.0 \\ \sigma= 0.5 \\ P(X>2) = 1 -P(X<2) \\ = 1 -P(Z< \frac{2-3}{0.5}) \\ = 1 -P(Z< -2) \\ = 1 -0.0227 \\ = 0.9773$