Chapter 7. Elite female runners are known to run the Boston Marathon (26.2 miles) in an average of 150 minutes with a standard deviation of

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Chapter 7. Elite female runners are known to run the Boston Marathon (26.2 miles) in an average of 150 minutes with a standard deviation of 7 minutes. Consider 18 marathons that are similar to the Boston Marathon. Let X represent the average of the 18 races. Unless specified, round all numbers to 2 decimal places. (HINT: You have to find the Standard error based on sample size in this problem).

1. X - ~ N( , ).
2. The probability (in % terms) that the runner will average between 147 and 152 minutes in these 18 marathons is %.
3. The 37th percentile for the average of these 18 marathons is minutes.
4. The first quartile of the average running times for these 18 marathons is minutes.