4. A company is planning to introduce to the market a new brand of soft drink. The dispensing machine fills the bottles with a volume following normal distribution with mean µ = 20 ounces and standard deviation ? = .5 ounces.

a. What is the probability that a randomly selected bottle from the production line contains more than 20.8 ounces of drinks?

b. A state regulation requires that the company labels each bottle showing the volume (in ounces) of soft drinks in the marketed bottles, and that no more than 2% of the bottles should contain less than the volume printed on the label. What volume should the company print on the label in order to comply with the regulation? (Round your answer to 1 decimal after the decimal point.)

5. The following game is offered in a casino. An employee flips a coin 12 times, but the player does not see the outcomes of these coin flips. After each flip of the coin the player has to guess whether the coin turned up head or tail. At the end the player receives k dollars, where k is the number of correct guesses, except that if she guesses all 12 coin flips correctly, then she will receive an additional 10,000 dollars (so in that case the total reward will be 10, 000 + 12 = 10, 012 dollars). Calculate the expected amount of winnings in this game

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?