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The distribution of college students’ commute time is skewed to the right with the mean 20...

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.

Math   Statistics-And-Probability   
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