Question

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 6.5 . You want your sample mean x¯ to estimate μ with an error of no more than 1.4 point in either direction.

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

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

Answer 1

soluhon The 68-95-99.7 in a empisical yule which 99.947. lies with in Thiee stanchi d in deviation PL M-30LKLU3-0-997 30=1.4 c:14 -0.4667 b) n=? m= ? 0.4 - (13.9285)? = 194.005 Tn=194

Answer 2

(a) 99.7% of all observations fall within 3 standard deviations, so we want 3??√=1.4$3$. Solving for ??√, we get that the standard deviation of ?
$\overline{x}$ must therefore be 0.4667 point.

(b) We need to choose 
$n$ so that 6.2?√=0.4667$\frac{6}{}$. This means ?⎯⎯√=13.285$\sqrt{n}=13.285$ , so ?=176.485. Because 176.485 must be a whole number, take ?=177.