Statistics

1. You’re on a game show and given the option of taking $800 cash or playing a dice game with the following rules. You will roll the dice 10 times. Each 1 that you roll you win $300, each 2 or 3 you roll you win $150, each 4 or 5 you roll you win $120 and every 6 you roll you lose $450 of your winnings.
Calculate the expected value for the dice game for any single roll.
(provide work)

2. Assume random guesses are being made for seven multiple choice questions with five possible answers on an SAT test.
What is the probability that the person guesses exactly 4 questions correctly?

3. The NFL releases suggesting the mean heights of players are normally distributed with a mean of 74.1 inches and a standard deviation of 0.72. Please determine the following:
Whats the probability that a player selected is under 6’3? (6’3 is 75 inches)

4. The NFL releases suggesting the mean heights of players are normally distributed with a mean of 74.1 inches and a standard deviation of 0.72. Please determine the following:
Whats the probability that a player selected is taller than 6’3? (6’3is 75 inches)

5. Data suggests that a randomly selected college student eats breakfast at a .3500 probability.
A)If 7 students are randomly selected determine the probability that the fourth student selected eats breakfast?
B)If 7 students are randomly selected determine the complement of the statement: At least one of the 7 students eats breakfast.  (This should be a statement not a calculation)
C)Determine the probability of the complement statement from the previous problem.
D)Using the probability from the previous problem determine the probability that at least one of the 7 students eats breakfast.