# Math Help - normal distribution

1. ## normal distribution

Can't figure out how to solve this for my math test due on Tuesday. Any help would be wonderful!

Testing indicates that the lifetimes of a new shipment of 500 storage batteries are approximately normally distributed with a mean of 2.5 years and a standard deviation of 0.4 years. How many of the storage batteries would you expect to last between 1.9 and 3.1 years?

2. (1.9 - 2.5)/0.4 =

(3.1 - 2.5)/0.4 =

If these formulas are not familiar to you, yiou need to back up a chapter and give it another go.

3. Originally Posted by MathIdiot
Can't figure out how to solve this for my math test due on Tuesday. Any help would be wonderful!

Testing indicates that the lifetimes of a new shipment of 500 storage batteries are approximately normally distributed with a mean of 2.5 years and a standard deviation of 0.4 years. How many of the storage batteries would you expect to last between 1.9 and 3.1 years?
Let X be the random variable lifetime of a battery.

X ~ Normal $(\mu = 2.5, \, \sigma = 0.4)$

Calculate p = Pr(1.9 < X < 3.1).

Let Y be the random variable number of batteries that last between 1.9 and 3.1 years.

Y ~ Binomial(n = 500, p = value from above)

Calculate E(Y).