figuring out a cutoff value

[half-life]

Hello

Since my teacher hasn't replied to any of my e-mails, I could use some help related to continuous probability distributions...

So we have a problem to solve related to expected job losses. The mean is 126,681, and the standard deviation is 30,000.

I figured out the first 2 parts of the problem, which were determining probabilities of the number of jobs lost for a couple scenarios. I used the formula z = x - mean / std deviation. Then I added the z values to get the probability.

Now, the last part of the problem says:

"What cutoff value will provide a .95 probability that the number of lost jobs will not exceed the value?"

I'm clueless. I looked at the z table under .95 and found .3289, but that doesn't help. If the mean is 126,681, then I need to figure out a number (probably higher than the mean) such that I could say, "There is a 95% probability that no more than ### jobs will be lost." If I just took the mean and divided it by .95, that seems to easy to really be the solution.

Can someone please help? Thank you.

[JohnM]

The z score corresponding to a probability of .95 (i.e., 95% of the area under the curve is below this z score) is 1.645, not .3289.