Question

The distribution of college students’ commute time is skewed to the right with the mean 20 minutes and the standard deviation 30 minutes.

1. Let X¯ be the sample mean commute time of a random sample of 9 students. What are (i) the mean and (ii) variance of X¯? (iii) Is the distribution of X¯ normal? (iv) Why or why not?

2. Let X¯ 100 be the sample mean commute time of a random sample of 100 students. What is the sampling distribution of X¯ 100? (State the (i) shape, (ii) mean, and (iii) standard deviation of X¯ 100).

3. The probability that mean commute time of a random sample of 100 students is greater than 17 minutes and less than a is 0.8. That is, P(17 < X¯ 100 < a) = 0.8. Find the value of a.

Answer #1

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select a random sample of 210 people from the 2000 U.S. Census who
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