A study of college football games shows that the number of holding penalties assessed has a mean of 2.2 penalties per game and a standard deviation of 0.9 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.25 penalties per game or more?Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

A company sells packages of cookies with the following promotion. If two cookies in a package are frostingless, you may get your money back. Suppose each cookie has a 1 100 chance of being frostingless and there are 20 cookies in a package.

(a) What is the expected number of frostingless cookies in a package? 5 packages?

(b) What is the variance in this number for one package? 5 packages?

(c) What is the probability of returning at least one package if you purchase 5?

An offline retail store called CoolStore have customers that are either students or not. Customers can buy a plastic bag or not. We know for a fact that: Twenty-five percent of all customers are students. Among customers that are students, eighty percent buy a plastic bag. Among customers who buy a plastic bag, fifty percent are students. Forty customers are chosen at random. The probability is one percent that the number of customers buying a plastic bag exceeds what number?

One buyer claims that 10% of 400 products are defective.

The manufacturer says that 2% of the products may be defective.

50 products will be checked.

Let the random variable be the number of broken out of the 50 items checked.

If X> c, accept what the buyer says.

if X < c, Accept what the manufacturer says.

Determine the number c in this decision rule so that when the buyer says it is true, the probability of rejection due to randomness does not exceed 5%.

A study of college football games shows that the number of holding penalties assessed has a mean 2.3 of penalties per game and a standard deviation 1.05 of penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.25 penalties per game or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

1. Contracts for two construction jobs are randomly assigned to one or more of three firms A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1 or 2 contracts.

2. (b) Find the marginal probability of Y1 and Y2.

3. (c) Are Y1 and Y2 independent? Why? (d) Find E(Y1 − Y2).

4. (e) Find Cov(Y1, Y2)

A study of college football games shows that the number of holding penalties assessed has a mean of 2.2 penalties per game and a standard deviation of 0.8 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.35 penalties per game or more? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

An ogre is very hungry but cannot decide how many chickens he wants to eat. So, he rolls a standard 6-sided die. Let Y be the number that he rolls. Then he goes to his chicken coop and randomly chooses Y chickens to eat. Suppose that his coop has 10 Rhode Island Reds and 4 Bantams.

(a) What is the probability that all of the Bantams get eaten? (b) What is the expected number of Bantams consumed?

A study of college football games shows that the number of holding penalties assessed has a mean of 2.2 penalties per game and a standard deviation of 1.05 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.15 penalties per game or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places