Question

11.	(15.28) Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μμ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.2. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 25. In answering the following, use z-scores rounded to two decimal places. If you choose one student at random, what is the probability (±±0.0001) that the student's score is between 20 and 30? You sample 29 students. What is the standard deviation (±±0.01) of sampling distribution of their average score x⎯⎯⎯x¯? What is the probability (±±0.0001) that the mean score of your sample is between 20 and 30?
12.	(15.30) 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 mean 377 minutes and standard deviation 66 minutes. The mean number of minutes of daily activity for lean people is approximately Normally distributed with mean 522 minutes and standard deviation 105 minutes. A researcher records the minutes of activity for an SRS of 7 mildly obese people and an SRS of 7 lean people. Usez-scores rounded to two decimal places or your calculator to answer the following: What is the probability (±±0.0001) that the mean number of minutes of daily activity of the 7 mildly obese people exceeds 420 minutes? What is the probability (±±0.0001) that the mean number of minutes of daily activity of the 7 lean people exceeds 420 minutes?
13.	(15.34) The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with mean 0.16 g/mi and standard deviation 0.053 g/mi. A company has 15 cars of this model in its fleet. What is the level L (±0.0001) such that the probability that the average NOX level x⎯⎯⎯x¯ for the fleet is greater than L is only 0.01?             L =
14.	(15.38) To estimate the mean score μμ 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 6.4. You want your sample mean x⎯⎯⎯x¯ to estimate μμ with an error of no more than 0.9 point in either direction. (a) What standard deviation (±±0.0001) must x⎯⎯⎯x¯ have so that 99.7% of all samples give an x⎯⎯⎯x¯ within 0.9 point of μμ? (b) How large an SRS do you need in order to reduce the standard deviation of x⎯⎯⎯x¯ to the value you found in part (a)?

Answer 1