# Statistics

In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all adults invest in mutual funds. Suppose a random sample of 25 stock investors is taken.

a. What is the probability that exactly seven are retired people?
b. What is the probability that 10 or more are retired people?
c. How many retired people would you expect to find in a random sample of 25 stock investors?
d. Suppose a random sample of 20 adults is taken. What is the probability that exactly seven adults invested in mutual funds?
e. Suppose a random sample of 20 adults is taken. What is the probability that fewer than six adults invested in mutual funds?
f. Suppose a random sample of 20 adults is taken. What is the probability that none of the adults invested in mutual funds?
g. Suppose a random sample of 20 adults is taken. What is the probability that 12 or more adults invested in mutual funds?
h. For parts e�g, what exact number of adults would produce the highest probability? How does this compare to the expected number

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2. Let X be the random variable denoting the number of retired people
a) P(X=7) = 25C7∗0.27∗0.818 = 0.1108
b) P(X>=10) =1-P(X<=9) Using the Binomdist() excel Function , which calculates P(X<=x) =1-.98266 = 0.0173
c)In a random sample of 25, the expected number is : 25*0.2 =5 Let Y be the random variable denoting number ofU.S. adults investing in mutual funds. Y~Bin(20,0.4)

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