# Probability Question

How to solve this question:

“A client will move his investment account unless the portfolio manager earns at least a 10% rate of return on his account. The rate of return for the portfolio that the portfolio manager has chosen has a normal probability distribution with an expected return of 19% and a standard deviation of 4.5%. What is the probability that the portfolio manager will keep this account?” from Kaplan Schweser

How many standard deviations below the mean is 10%?

10% is 2 standard deviations (2 times 4.5%) below the mean (19%). Approximately 2% of the normal distribution has values below/to the left of mean-2*standard deviation. So the answer to your question is 98%.

Thanks for the reply… i was trying to use : TEST Stats =( Sample Stat - Hypotheses Value (Mean)/ Std error )… So in this case (10-19/ STD Error.)

But sample size is not mentioned…So, can I use (10-19/std(4.5)).

What am I missing??

He has one chance to keep the account: the sample size is 1.

“One Chance” : Thanks.

My pleasure.