To estimate the mean score of those who took the Medical College Admissions Test

Question

To estimate the mean score of those who took the Medical College Admissions 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 to estimate with an error of no more than 1 point in either direction.
(a) What standard deviation must x have so that 99.7% of all samples give an x within 1 point of ? (Use the 68-95-99.7 rule. Round your answer to four decimal places.) points
(b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found in part (a)? (Round your answer up to the next whole number.)    To estimate the mean score of those who took the Medical College Admissions 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 to estimate with an error of no more than 1 point in either direction.
(a) What standard deviation must x have so that 99.7% of all samples give an x within 1 point of ? (Use the 68-95-99.7 rule. Round your answer to four decimal places.) points
(b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found in part (a)? (Round your answer up to the next whole number.)    To estimate the mean score of those who took the Medical College Admissions 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 to estimate with an error of no more than 1 point in either direction.
(a) What standard deviation must x have so that 99.7% of all samples give an x within 1 point of ? (Use the 68-95-99.7 rule. Round your answer to four decimal places.) points
(b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found in part (a)? (Round your answer up to the next whole number.)   

Explanation / Answer

A) so we want 3*stdev = 1

stdev = 1/3 = .33

B) stdev of mean = stdev/sqrt(n)

n = (6.4/.33)^2=376

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