Question

Question 19 (8 points) Determine in each of the following situations whether the Central Limit Theorem applies in order to conclude that sampling distribution of the sample mean, that X-NI 7-N (M, ) For each distribution, determine whether CLT applies. If it does not, then enter NA as your answer in the blank number that corresponds to the distribution number. If it does, then enter the shape of the sample means as your first item in a list, the mean of the sample means as your second item in a list, and the standard deviation of the sample means as your third item in a list, answers separated by commas and with no extra spaces. Do not enter any units or commas as part of large numbers, and if rounding is necessary, then do so to two decimal places. For example, a valid answer could look like normal, 25,2.21. Another valid answer could look like skewed, 25,7. Distribution 1: The distribution of American households has a mean of 2.4 people and a standard deviation of 1.4 people. The U.S. Census Bureau compiled information using a random sample of 225 homes. Do you know anything about the sampling distribution of the sample means coming from repeatedly taking samples of size 225 from the population of American households? Distribution 2: The distribution of weights of tennis balls manufactured from a certain machine is Normal with a mean of 57.6 grams and a standard deviation of 0.3 grams. A simple random sample of size 9 is to be selected and the sample mean weight computed. Do you know anything about the sampling distribution of the sample means coming from repeatedly taking samples of size 9 from the population of tennis balls manufactured by this machine?

Answer 1

1) normal,2.4,0.093

2) normal,57.6,0.1

3) skewed, 7,0.158

4) normal,540000,4000

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