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You have $460,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $180,000. Consider the summary measures in the following table:

Investment Expected Return Standard Deviation
Old portfolio 8 % 12 %
House 19 % 23 %

The correlation coefficient between your portfolio and the house is 0.33.

a. What is the expected return and the standard deviation for your portfolio comprising your old portfolio and the house? (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

Expected return %
Standard deviation %

b. Suppose you decide to sell the house and use the proceeds of $180,000 to buy risk-free T-bills that promise a 14% rate of return. Calculate the expected return and the standard deviation for the resulting portfolio. [Hint: Note that the correlation coefficient between any asset and the risk-free T-bills is zero.] (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

Expected return %
Standard deviation %

At a local community college, 43% of students who enter the college as freshmen go on to graduate. Seven freshmen are randomly selected.

a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)

Probability

. What is the probability that at most six will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)

Probability

c. What is the expected number that will graduate? (Round your final answer to 2 decimal places.)

Expected number

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