# standard deviation

#### saige30

##### New Member
I have a problem I'm struggling to figure out how to compute....could someone walk me though the problem and explain how to figure out the answer? I'm really not even sure where to start on these types of problems. Thanks!

problem: The average sales representative for Insmed pharmaceutical company earns $124,000 in sales incentives with a standard deviation of$32,000. Assuming that the salaries are normally distributed, 90% of teh salaries will be above what dollar mark?

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#### Dragan

##### Super Moderator
I have a problem I'm struggling to figure out how to compute....could someone walk me though the problem and explain how to figure out the answer? I'm really not even sure where to start on these types of problems. Thanks!

problem: The average sales representative for Insmed pharmaceutical company earns $124,000 in sales incentives with a standard deviation of$32,000. Assuming that the salaries are normally distributed, 90% of teh salaries will be above what dollar mark?
Use the Z-tranformation: Z = (X - Mu)/Sigma.

You know that Mu = 124, Sigma = 32, and from the Z-table Z = -1.28. Solving for X we obtain X = 32*(-1.28) + 124= your answer...(multiply your answer times 1000 to get the dollar amount).

#### saige30

z score

thanks so much...my answer is 90% of scores will be over $83,040. Is that correct? also- I knew equation already, but I wasn't sure how to find the zscore. I have the table in my book, but my professor didn't discuss how to use it. Can you offer any help there? THanks! #### Dragan ##### Super Moderator I have the table in my book, but my professor didn't discuss how to use it. Can you offer any help there? THanks! Your question would be much easier for me to address if I had your textbook and then I could just (simply) show you....but I don't. How about this...Why not ask your professor to show you how to use the table(s) - since it seems to be the case that you're being required to solve these problems. #### saige30 ##### New Member i would if only he had office hours from when he assigned the practice through tomorrow (our test) but he's out of the office thanks though for your help!! #### Mean Joe ##### TS Contributor problem: The average sales representative for Insmed pharmaceutical company earns$124,000 in sales incentives with a standard deviation of \$32,000. Assuming that the salaries are normally distributed, 90% of teh salaries will be above what dollar mark?

You want the area under the curve = .90. This is a one-tail problem; the z-score corresponding to a tail area of .10 is z=1.282 BUT since we want the area ABOVE the value, we use z=-1.282

(Look at your insurance problem where they wanted to cover 85% BELOW the specific value and you used the positive z. Understand when to use positive z and when to use negative z? You won't get the right answer if you don't.)

Using the formula (for one-tail): z = (x - mean) / stdev, we can solve x=82,976.