Question

A company produces light bulbs whose life follows a normal distribution with a mean of 1,200

hours and standard deviation 200 hours. If we choose a light bulb at random, what is the

probability that its lifetime will be between 1100 and 1,600 hours?

Answer 1

$\mu=1200$

$\sigma=200$

$P(1100<X<1600)=$

$=P(\frac{1100-\mu}{\sigma}<Z<\frac{1600-\mu}{\sigma})=$

$=P(\frac{1100-1200}{200}<Z<\frac{1600-1200}{200})=P(-0.5<Z<2)=$

$=P(Z<2)-P(Z<-0.5)=0.9772-0.3085=0.6687$

Answer: 0.6687 is probability that its lifetime will be between 1100 and 1,600 hours