According to the U. National Weather Service, at any given moment of any day, approximately 2000 thunderstorms are occurring worldwide. Many of...

1. According to the U.S. National Weather Service, at any given moment of any day, approximately 2000 thunderstorms are occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. Twelve days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was x̄ = 8.6 million. Assume the distribution of the number of lightning strikes per day is normal with σ = 0.35 million. Please use 4 decimal places for all critical values.

(1 pt.) a) What assumptions are required so that you can construct a confidence interval for the mean number of lightning strikes per day?

(1 pt.) b) Find a 99.8% confidence interval for the mean number of lightning strikes per day.

(1 pt.) c) Interpret your answer in part b).

(1 pt.) d) Determine the number of days that need to be sampled to ensure that the half-width of the interval in b) is at most 0.1 million.

Additional Problems: 8.31 (p.350), 8.33 (p.350), 8.35 (p.350), 8.39 (p.351)

Practice Problems: 8.55 (p.360), 8.57 (p.360), 8.59 (p.360)

2. One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 18 with a sample mean of 201.2 lbs. and a sample standard deviation of 11.8 lbs. Assume that the distribution of the weights is normal. Please use 4 decimal places for all critical values.

(1 pts.) a) Find the 95% confidence interval for the true mean weight of the players from the Detroit Red Wings.

(2 pts.) b) Calculate the 95% lower bound of the true mean weight of the players from the Detroit Red Wings. Please interpret your result.

(1 pt.) c) Why is the lower limit from part b) different from the lower bound in part a)? Please explain your answer by listing the symbols that are different between parts a) and b) and explain why the symbols are used.

(1 pt. BONUS) d) The 95% confidence interval of the weights for the Boston Bruins is (194.16, 205.81).