Thread: Z-Table w/Percentage Question

The monthly sales of mufflers in the Richmond, VAarea follow a normal distribution, with a mean of 1,200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is no more than a 5% chance of running out of stock. What level should the manufacturer select as the minimum inventory level?

I know this includes the z-table, but I am completely lost!!!

Please help!!!

Originally Posted by kendrick02

The monthly sales of mufflers in the Richmond, VAarea follow a normal distribution, with a mean of 1,200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is no more than a 5% chance of running out of stock. What level should the manufacturer select as the minimum inventory level?

I know this includes the z-table, but I am completely lost!!!

Please help!!!

You need the value of x* such that Pr(X < x*) = 0.05.

Use your tables to get the value z* of Z such that Pr(Z < z*) = 0.05. Then from Z = (X - mu)/sigma you have z* = (x* - 1200)/225. Substitute the value of z* that you found into this. Solve for x*.