Answer to Question #308935 in Statistics and Probability for cionee

Question

A certain type of storage battery lasts, on average, 3.0 years with a standard deviation of 0.5 year. Assuming that the battery lives are normally distributed, find the probability that a given battery will last less than 2.3 years.

Answer 1

Let X be the battery lifetime, $X\sim N\left( 3,0.5^2 \right)$

Then

$P\left( X\leqslant 2.3 \right) =P\left( \frac{X-3}{0.5}\leqslant \frac{2.3-3}{0.5} \right) =P\left( Z\leqslant -1.4 \right) =\\=\varPhi \left( -1.4 \right) =0.08076$