# Probability based on Z score.

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1.According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard deviation of the annual return was 24.5%; During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%.; The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric.; Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

a. Find the probability that the return for common stocks will be greater than 0%.

b. Find the probability that the return for common stocks will be less than 20%.

4.A large candy manufacturer is concerned that the mean weight of their bag of Gooey Sour Worms is not greater than 7.3 ounces.; It can be assumed that the population standard deviation is .5 ounces based on past experience.; A sample of 169 gummy worms is selected and the sample mean is 7.35 ounces.  Using a level of significance of .10, is there evidence that the population mean weight of the candy bars is greater than 7.3? Fully explain your answer.

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#### Solution Summary

The solution gives the complete steps involved in the calculation probability of the events specified in the question.