Question

To estimate the mean score μ 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 6.2 . You want your sample mean ¯ x x¯ to estimate μ μ with an error of no more than 1.4 1.4 point in either direction. (a) What standard deviation must ¯ x x¯ have so that 99.7 % 99.7% of all samples give an ¯ x x¯ within 1.4 1.4 point of μ μ ? Use the 68 – 95 – 99.7 68–95–99.7 rule. (Enter your answer rounded to four decimal places.

Answer 1

Answer: 0.4667

Step-by-step explanation:

According to 68–95–99.7 rule , About  99.7% of all data values lies with in 3 standard deviations from population mean ($\mu$).

Here , margin of error = 3s , where s is standard deviation.

As per given , we have want our sample mean $\overline{x}$ to estimate μ μ with an error of no more than 1.4 point in either direction.

If 99.7% of all samples give an $\overline{x}$ within 1.4 , it means that

$3s=1.4$

Divide boths ides by 3 , we get

$s=0.466666666667\approx0.4667$

Hence, So $\overline{x}$ must have 0.4667 as standard deviation so that 99.7 % 99.7% of all samples give an $\overline{x}$ within 1.4 point of μ .