# Normal Probability Problems

I need assistance with problems: 6.51, 6.52 and 6.53 in the attached document.

Please use excel.

6.51 All the major stock market indexes posted heavy losses in 2008. The mean one year return for stocks in the S&P 500, a group of 500 very large companies, was -38.5%. The mean one-year return for the NASDAQ, a group of 3200 small and medium-sized companies, was -40.5%. Historically, the one-year returns are approximately normal, the standard deviation in the S&P 500 is approximately 20%, and standard deviation in the NASDAQ is approximately 30%.

a. What is the probability that a stock in the S&P 500 gained value in 2008?

b. What is the probability that a stock in the S&P 500 gained 10% or more?

c. What is the probability that a stock in the S&P 500 lost 50% or more in 2008?

d. What is the probability that a stock in the S&P 500 lost 60% or more?

e. Repeat (a) through (d) for a stock in the NASDAQ.

f. Write a short summary on your findings. Be sure to include a discussion of the risks with a large standard deviation.

6.52 An article reported that (L. J. Flynn, "Tax Surfing," The New York Times, March 25, 2002, p. C10) that the mean time to download the home page for the Internal Revenue Service, www.irs.gov, is 0.8 seconds. Suppose that the download time is normally distributed, with a standard deviation of 0.2 seconds. What is the probability that a download time is

a. less than 1 second?

b. between 0.5 and 1.5 seconds?

c. above 0.5 second?

d. Above how many seconds are 99% of the download times?

e) 95% of the download times are between what two values, symmetrically distributed around the mean?

6.53 The same article mentioned in Problem 6.52 also reported that the mean download time for H&R Block Web site, www.hrblock.com, is 2.5 seconds. Suppose that the download time is normally distributed, with a standard deviation of 0.5 second. What is the probability that a download time is

a. less than 1 second?

b. between 0.5 and 1.5 seconds?

c. above 0.5 second?

d. Above how many seconds are 99% of the download times?

e. Compare the results for the IRS site computed in Problem 6.52 to those of the H&R Block site.

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#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

Probability of Error

A voltmeter is used to measure a known voltage of 100 V. Forty percent of the readings are within 0.5 V of the true value. Estimate the standard deviation for the meter. What is the probability of an error of 0.75 V?

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