# Statistics for Managers

See attached file for problem 2.

1. Can the problem title "basic probability" be solved using excel? If yes, please explain step-by-step on excel. Please also include any formulas and how you reach the conclusion. For this question, disregard part d.

In 37 of the 59 years from 1950 through 2008, the S&P 500 finished higher after the first 5 days of trading. In 32 of those 37 years, the S&P 500 finished higher after the first 5 days of trading. In 32 hours of those 37 years, the S&P 500 finished higher for the year. Is a good first week a good omen for the upcoming year? The following table gives the first-week and annual performance over this 59-year period:

S&P 500's Annual Performance

First Week Higher Lower

Higher 32 5

Lower 11 11

a. If a year is selected at random, what is the probability that the S&P 500 finished higher for the year?

b. Given that the S&P 500 finished higher after the first 5 days of trading, what is the probability that it finished higher for the year?

c. Are the two events "first-week performance" and "annual performance" independent? Explain.

d. Look up the performance after the first 5 days of 2009 and the 2009 annual performance of the S&P 500 at finance.yahoo.com. Comment on the results.

2. In the excel attachment titled week2, can you please explain to me how to interpret the simple and joint probability and also the addition rule?

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#### Solution Summary

Complete, Neat and Step-by-step solution provided. Simple and Joint Probability interpretation included for Problem 2.