According to the National Weather Service, at any given moment of any day, there

Question

According to the National Weather Service, at any given moment of any day, there are approximately 2000 thunderstorms occurring worldwide. Many of these storms include lightning strikes. Sensitive electronic equipment is used to record the number of lightning strikes worldwide every day. Ten days were selected at random, and the number of lightning strikes on each day was recorded. The sample mean was x = 8.6 million. Assume the distribution of the number of lightning strikes per day is normal with = 0.35 million. Fill in the blanks. (Give your answers to four decimal places.)

A 99% confidence interval for the mean number of lightning strikes per day worldwide is (, ).

Explanation / Answer

Since we are dealing with a population with some mean and a finite variance and since n 30, we can state that the sampling distribution is normal because of CLT. Since the days are selected randomly, we can assume SRS. = 8.6 (2.3263) 0.35 30 = 8.6 .1487 = 8.45. We are 99% confident that the true average number of lightning strikes on any given day is greater than 8.45 million. 3 Commented [LAF3]: 1 pt.: assumptions: required n is 30. the comment about SRS is not required. However, please comment if it is not there. 1 pt. work: be sure that there is a '-': 0.2 pts, and the correct critical value is there: 0.2 pts. 1 pt. interpretation: 0.2: confidence level, 0.2: the word population or true. 0.2: the word mean or average, 0.2: what the average is of (in this case, they have to include number of lightning strikes), 0.1: the word greater, 0.1: the value. 'million' is not required, but comment if it is not there

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