Statistics Problem

On the practice test:

A stock portfolio’s returns are normally distributed. It has had a mean annual return of 25% with a standard deviation of 40%. The probability of a return between -41% and 91% is closest to:

A) 65%

B) 90%

C) 95%

I put down C, when the answer is B. When I check the Z-score table, a -1.65 and 1.65 z-score covers 95.05% of the data. Can somebody explain to me the correct way to reason through this? Thanks.

You’re misreading the Z-score table.

If you have a table that lists 0.9505 for the Z-value of 1.65, that table is giving you the probability that the value is less than +1.65; i.e., that it lies between -∞ and +1.65. It isn’t saying that the probability is 0.9505 that the value lies between -1.65 and +1.65. That probability is 0.90, or 90%. (Well, 90.10%, but it’s close enough.)

Ahhhh got it. It’s been awhile since I’ve taken stats, so I forgot that the positive z-score table refers to the range from negative infinity to the z-score. Should cut the area in half and subtract out the portion not covered by the z-score and double that. Thanks!

My pleasure.