Suppose that the mean of the annual return for common stocks

Probability   1.  Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 7.2%, and the standard deviation of the annual return was 31.2%.  Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 1.6%, and the standard deviation was 7.0%.  The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario.  Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously. Find the probability that the return for common stocks will be greater than 3.5%. Find the probability that the return for common stocks will be greater than 10%. Hint:  There are many ways to attack this problem in the HW. If you would like the normal distribution table so you can draw the pictures (my preferred way of learning) then I suggest you bookmark this site: http://www.statsoft.com/textbook/sttable.htmlhttp://www.statsoft.com/textbook/sttable.html common stock mean= 7.25 SD= 31.25 Find the probability that the return for common stocks will be greater than 3.5%. Z= (3.5 -7.25) /31.25= -0.12 Pr(X = 3.5) = Pr(Z = (3.5 - 7.25)/31.25  ) = Pr(Z = -0.12) = 1 - 0.4522 = 0.5478 Find the probability that the return for common stocks will be greater than 10%. Z= (10-7.25 ) /31.25 P(z>10) = 0.088 Therefore, Pr(X = 10) = Pr(Z = (10 - 7.25)/31.25  ) = Pr(Z = 0.088) = 1 - 0.5351 = 0.4649 Confidence Interval Estimation   2. Compute a 95% confidence interval for the population mean, based on the sample 50, 54, 55, 51, 52, 51, 54, 52, 56, and 53.  Change the last number from 53 to 91 and recalculate the confidence interval.  Using the results, describe the effect of an outlier or extreme value on the confidence interval.   Mean= 52.8 SD = 1.93 N= 10 At 95% confidence interval,