Please type your answer (4 points) 2. According to the U.S. National Weather Ser
ID: 3056227 • Letter: P
Question
Please type your answer
(4 points) 2. 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 8.6 million. Assume the distribution of the number of lightning strikes per day is normal with = 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.Explanation / Answer
a) Number of lightning strikes per day follows Normal distribution with mean 8.6 and standard deviation is 0.35
b) 99.8% confidence interval = [xbar ± Z critical */n] = [8.6 ± 3.0902 * 0.35/12] = [8.29, 8.91]
c) It is 99.8% confidence that population mean of lightning strikes per day lies between above interval.
d) sample size (n) = (3.0902 * 0.35/0.1)2 = 117