3 stats qs

Learning Goal: I’m working on a statistics question and need an explanation and answer to help me learn.

7. Exactly 100 employees of a firm have each purchased one ticket in a lottery, with the drawing to be held at the firm’s annual party. Of 40 men who purchased a ticket, 25 are single. Only 9 of the women who purchased a ticket are single.

(a) Complete a probability table for this situation.

(b) If the winner is single, what is the probability that she is a woman?

(c) If the winner is married, what is the probability that he is a man?

8. The percentage of undergraduate students in the United States receiving federal financial aid is 60%. Consider a random sample of 50 such students. Let X be the number of students in the sample who receive financial aid.

(a) Calculate the mean and the standard deviation of X.

(b) What is the probability that in the random sample at least 32 students receive financial aid?

(c) Find the largest value for w such that the probability that at least w students in the sample receive financial aid is larger than 95%.

9. Before negotiating a long-term construction contract, building contractors must carefully estimate the total cost of completing the project. For a particular construction project it is assumed that the total cost, X, is normally distributed with mean $900,000 and standard deviation $170,000. The revenue, R, promised to the contractor is $1,000,000.

(a) The contract will be profitable if revenue exceeds total cost. What is the probability that the contract will be profitable for the contractor?

(b) Suppose that the contractor has the opportunity to renegotiate the contract. What value of R should the contractor strive for in order to have a .99 probability of making a profit?

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