Charlie’s portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. Assume his investment return

Question

4 years ago

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Charlie’s portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. Assume his investment return

s 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.

Mathematics

1 answer:

Deffense [45] · Answer 1 · 2022-01-21T08:27:45+03:00

Answer:

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

Step-by-step 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.