Answer to Question #255201 in Statistics and Probability for Mary

Question

The life span of electric bulbs is normally distributed with mean of 1860 hours and the SD of 68 hours. Estimate the percentage of lamps which are expected to burn between 1780 hours and 1920 hours

Answer 1

We have $E=1860,\ \sigma=68$ . Use Laplace function:

$P(a<X<b)=\Phi(\frac{b-E}{\sigma})-\Phi(\frac{a-E}{\sigma})$

Substitute $a=1780,\ b=1920$ and $M$ and $\sigma$:

$P=\Phi(\frac{1920-1860}{68})-\Phi(\frac{1780-1860}{68})\approx 0.6906$