Some variable of interest follows a (normal/right-skewed) distribution with a me

Question

Some variable of interest follows a (normal/right-skewed) distribution with a mean of 100 and a standard deviation of 10. In a random sample of size (5/50), suppose you are interested in calculating the probability that the sample mean is between 95 and 120. (You do not need to actually calculate the probability for this question.) In which of the following situations (select more than one if appropriate) is it possible to calculate the probability, and if it is possible to calculate the probability, would the calculated probability be exact or approximate? [For example, the first option below says "normal, 5, and exact". For this option, consider if we have a variable following a normal distribution and we take a random sample of size 5. In this situation, if it is not possible to calculate the probability of interest, you would not check the box. If it is possible to calculate the probability of interest, you have to assess if the calculated probability is exact or approximate. Then follow the same procedure for each of the options.] Question 1 options: A) normal, 5, and exact B) normal, 5, and approximate C) normal, 50, and exact D) normal, 50, and approximate E) right-skewed, 5, and exact F) right-skewed, 5, and approximate G) right-skewed, 50, and exact H) right-skewed, 50, and approximate

Explanation / Answer

A) normal, 5, and exact

C) normal, 50, and exact

H) right-skewed, 50, and approximate

are correct

Note H) is correct due to central limit theorem

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