Question

Charlie’s portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. Assume his investment returns follows a normal distribution.What is the probability that the actual return will be between the mean and one standard deviation above the mean?Use 2 decimal points.

Answer 1

There is a 34.13% probability that the actual return will be between the mean and one standard deviation above the mean.

Explanation:

This is problem is solving using the Z-score table.

The Z-score of a measure measures how many standard deviations above/below the mean is a measure. Each Z-score has a pvalue, that represents the percentile of a measure.

What is the probability that the actual return will be between the mean and one standard deviation above the mean?

One measure above the mean is
`Z = 1`

The mean is
`Z = 0`

This means that this probability is the pvalue of
`Z = 1` subtracted by the pvalue of
`Z = 0`.

`Z = 1` has a pvalue of 0.8413.

`Z = 0` has a pvalue of 0.50.

This means that there is a 0.8413-0.50 = 0.3413 = 34.13% probability that the actual return will be between the mean and one standard deviation above the mean.