Question

The length of life of an instrument produced

by a machine has a normal distribution with a

mean of 12 months and standard deviation of

2 months. Find the probability that an

instrument produced by this machine will last

a) less than 7 months.

b) between 7 and 12 months.

Answer 1

a)

$z=\frac{x-\mu}{\sigma}=\frac{7-12}{2}=-2.5$

$P(x<7)=(z<-2.5)=0.0062$

b)

$z_1=\frac{x_1-\mu}{\sigma}=\frac{7-12}{2}=-2.5$

$z_2=\frac{x_2-\mu}{\sigma}=\frac{12-12}{2}=0$

$P(7<x<12)=P(z_1<z<z_2)=$

$=P(x<12)-P(x<7)=0.5-0.0062=0.4938$