Assume that the heights of 30,000 male students at a university are normally distributed with a mean of 68.0 inches and a standard deviation of 3.0 inches. A random sample of 35 students is taken and the mean is calculated.

Round your z-scores to 2 decimal places during your calculations, then round probability answers to 3 decimal places

1. What is the probability that this mean value will be between 66.8 inches and 68.8 inches?

You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. Round your z-scores to 2 decimal places during your calculations, then round probability answers to 2 decimal places

2. You play this game five times. Find the expected value of your average winnings from 5 games.

3. You play this game five times. Find the standard deviation of your average winnings of 5 games.

Carbon monoxide (CO) emissions for a certain kind of car vary with mean 2.9 g/mi and standard deviation 0.4 g/mi. A company has 80 of these cars in its fleet. Let represent the mean CO level for the company's fleet.

4. Estimate the probability that is between 3.0 and 3.1 g/mi. Round probability answer to 6 decimal places

HINT:P(Z<4.47) = 0.99999206493023(use exactly this number in your calculations)

5. There is only a 5% chance that the fleet's mean CO level is greater than what value? z-score corresponding to top 5% is z = 1.645 Round to 2 decimal places.