# Math Help - Normal Distribution Help!!

1. ## Normal Distribution Help!!

The mean lifetime of a wrist watch is 25 months, with a standard deviation of 5 months, the distribution is normal. For how many months should a guarantee be made if the manufacturer doesnt want to exchange more than 10% of the watches?

Im having trouble in understanding how to figure out the area under the distribution for this, calculating is fine.

2. Originally Posted by lynchjp50
The mean lifetime of a wrist watch is 25 months, with a standard deviation of 5 months, the distribution is normal. For how many months should a guarantee be made if the manufacturer doesnt want to exchange more than 10% of the watches?

Im having trouble in understanding how to figure out the area under the distribution for this, calculating is fine.
You require the value of x* such that Pr(X < x*) = 0.1.

Use your standard normal tables in reverse to find the value of z* such that Pr(Z < z*) = 0.1.

Then from $Z = \frac{X - \mu}{\sigma}$ you have $z^* = \frac{x^* - 25}{5}$.

Substitute the value of z* and solve for x*.