A financial advisor knows that the annual returns for a particular investment follow a normal distribution with mean 0.066 and standard deviation 0.04. Using the 68-95-99.7 rule, what would be the most that a client who is interested in the investment could reasonably expect to lose, to three decimal places?

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Mathematics

Kailee Johns

20 July, 17:21

A financial advisor knows that the annual returns for a particular investment follow a normal distribution with mean 0.066 and standard deviation 0.04. Using the 68-95-99.7 rule, what would be the most that a client who is interested in the investment could reasonably expect to lose, to three decimal places?

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Long · Answer 1

the client could expect a maximum loss of - 0.054/year (-5,4%/year)

Step-by-step explanation:

since the 68-95-99.7 rule states that states probability that the anual return stays between 1 standard deviation from the mean is 68%, 2 standard deviations → 95% and 3 standard deviations → 99.7%

Then we are almost certain that the annual return will stay between 3 standard deviations from the mean.

Thus the most a client can loose is approximately at 3 standard deviations from the mean = 0.066 - 3*0.04 = - 0.054 (-5,4%/year)