[silvergray545]

I've run into a problem that I can't seem to figure out. I'm working on a case study that deals with normal distribution. Our professor wants us to use excel to get our answers but when I put the formula in excel, I get a different answer than I do by doing it by hand. I'll explain.

The mean and standard deviation are already given. There are a few numbers that you need to plug in for X. The excel command is =NORMDIST(x,mean,standard deviation,1)

To solve it by hand, you need to find the z score with the given values. The formula for that is z = (x-mean)/standard deviation then you take the z score and look it up on the chart to find the percentage.

With that being said, I'll give you an example of one of the problems. x = 20%, mean = 8.8% and the standard deviation = 5.98%.

Plug the values into excel and the answer is 0.969459572.

Do the math by hand (.2-.088)/.0598 which gives you a z score of 1.87. Then look it up on the chart and it is .4693

.97 and .47 are two completely different numbers. Anybody know what I'm doing wrong?

Below is the assignment if you need further clarification. Thanks

"Question One (twenty points)
You are hired as a consultant by the Alliance Financial Company. Alliance’s chief financial officer (CFO), Ms. Gail Roberts, has asked you to aid her in determining the appropriateness of a number of different investment categories for several Alliance customers. The table below shows the mean return and the standard deviation for nine different investment classes of investments sold by Alliance over the last 10 years. It is known that the returns follow a normal distribution.

Investment class Mean Return (%) Standard Deviation (%)
Fixed annuities 8.31 0.54
Cash equivalents 7.73 0.81
U.S. Treasury bonds 8.80 5.98
U.S. Investment-grade corporate bonds 9.33 7.92
Non-U.S. government bonds 10.95 10.47
Domestic large cap stocks 11.71 15.30
International equities 14.02 17.16
Domestic mid-cap stocks 13.64 18.19
Domestic small cap stocks 14.93 21.82

(i) Ms. Roberts has asked you to develop a table with some information that could be used in generating recommendations for different customers. Specifically, what she would like to know for each investment class is: what is the probability of a return for
(1) Greater than 5%,
(2) Greater than 20%,
(3) Greater than 50%,
(4) A loss (a return of less than 0)
(5) A loss of more than 10%, and
(6) A loss of more than 20%

Summarize the results in a table format"