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To estimate the mean score ?μ of those who took the Medical College Admission Test on...

To estimate the mean score ?μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.2. You want your sample mean ?¯ to estimate ?μ with an error of no more than 1.4 point in either direction.

(a) What standard deviation must ?¯ have so that 99.7% of all samples give an ?¯within 1.4point of ?μ ? Use the 68–95–99.7rule. (Enter your answer rounded to four decimal places.)

standard deviation of ?¯=

(b) How large an SRS do you need in order to reduce the standard deviation of ?¯ to the value you found? (Enter your answer rounded to the nearest whole number.)

SRS size ==

It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately Normally distributed with 367 minutes and standard deviation 64 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with 525 minutes and standard deviation 110 minutes. A researcher records the minutes of activity for an SRS of 8 mildly obese people and an SRS of 8 lean people.

(a) What is the probability that the mean number of minutes of daily activity of the 8 mildly obese people exceeds 400 minutes? (Enter your answer rounded to four decimal places.)

probability:

(b) What is the probability that the mean number of minutes of daily activity of the 8 lean people exceeds 400minutes? (Enter your answer rounded to four decimal places.)

probability:

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