# Normal probability distribution of investments

An investment broker reports that the yearly returns on common stocks are approximately normally distributed with a mean return of 12.4 percent and a standard deviation of 20.6 percent. On the other hand, the firm reports that the yearly returns on tax-free municipal bonds are approximately normally distributed with a mean return of 5.2 percent and a standard deviation of 8.6 percent.

(a) Use the investment broker's report to estimate the maximum yearly return that might be obtained by investing in tax-free municipal bonds. (Round your answer to the nearest whole percent.)

Maximum yearly return ___%

(b) Find the probability that the yearly return obtained by investing in common stocks will be higher than the maximum yearly return that might be obtained by investing in tax-free municipal bonds. (Round your answer to 4 decimal places.)

P = ____

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Let X denotes the yearly returns on common stocks and Y denotes the yearly returns on tax-free municipal bonds.

It is given that,

X is normally distributed with mean μ = 12.4 and standard deviation σ = 20.6.

Y is ...

#### Solution Summary

Normal probability distributions of investments are examined. The maximum yearly return that might be obtained by investing in tax-free municipal bonds are given.