Answer each question.Show your work for every example.

1.Suppose I roll two six-sided dice and offer to pay you $10 times the sum of the numbers showing. (e.g., if I roll a 4 and a 5, I will pay you $10 * (5+4) = $90). The probability chart for each roll is given:

Roll 2 Probability 0.027778Roll 3 Probability 0.055556Roll 4 Probability 0.083333 Roll 5 Probability 0.111111Roll 6 Probability 0.138889

Roll 7 Probability 0.166667 Roll 8 Probability 0.138889Roll 9 Probability 0.111111Roll 10 Probability 0.083333 Roll 11 Probability 0.055556

Roll 12 Probability 0.027778

A)What is the expected payoff to you?

B)What is the variance of the payoff to you?

C)What is the standard deviation of the payoff to you?

2.Now we are going to play the game 100 times. Each time I will pay you $100 times the

A)What is the expected total payment to you (the sum of all 100 games)?

B)What is the standard deviation of your payout?

C)What is the probability you will earn more than $6200?

D)What is the probability you will earn less than $7200?

E)What is the probability you will earn between $6400 and $6850?

3.The number of people who show up to New York Yankees games can be approximated as a Normal distribution, with an average of 34,000, and a standard deviation of 4,000.

A)What is the probability that more than 40,000 people will come to any one specific game?

B)What is the probability that less than 30,000 people will come to any one specific game?

C)What is the probability that between 33,000 and 37,000 will be at any one specific game?

4.Suppose the average height of American adult males is 5 feet 10 inches (70 inches) and the standard deviation is 3 inches. If I randomly sample 100 men:

A)What will the expected value of the average height of that sample be? (i.e. the mean of the sampling distribution)

B)What will the standard deviation of the average height in that sample be? (i.e. the standard deviation of the sampling distribution)

C)How big of a sample would we need to have a standard deviation of 0.1 inches?