Question

What is the probability that the shelf life of the battery is between 400 days and 550 days?

Answer 1

A certain type of battery has a mean shelf life of 600 days with a standart deviation of 28 days.

The probability that 400<X<550 is equal to the blue area under the curve.

Since $\mu=600$  and $\sigma=28$  we have:

$P(400<X<550) = P(400-600<X-\mu<550-600)\\=P(\frac{400-600}{28}<\frac{X-\mu}{\sigma}<\frac{550-600}{28})$

Since 

$\frac{x-\mu}{\sigma} = Z$ , $\frac{400-600}{28} = -7.14$ and $\frac{550-600}{28} = -1.79$  we have:

$P(400<X<550)=P(-7.14<Z<-1.79)$

Use the standard normal table to conclude that:

$P(-7.14<Z<-1.79)=P(-1.79)-P(-7.14)=0.03673-0=0.03673$

Answer: 0.0367.