To estimate the mean score ? 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 ?¯ to estimate ? with an error of no more than 0.9  point in either direction.(a) What standard deviation must ?¯ have so that 99.7% of all samples give an ?¯ within 0.9 point of ? ? 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=

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Asked Nov 1, 2019
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To estimate the mean score ? 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 ?¯ to estimate ? with an error of no more than 0.9  point in either direction.
(a) What standard deviation must ?¯ have so that 99.7% of all samples give an ?¯ within 0.9 point of ? ? 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=
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Expert Answer

Step 1

Part-a
Given
Standard deviation = 6.5
According to 68-95-99.7 rule with in one standard deviation of mean there is 68% of data, with in two standard deviations of mean there is 95% of data, with in three standard deviations of mean there is 99.7% of data.

So the three standard deviations away from mean will have 99.7% of data.

Step 2

The given distance from mean on either sides = 0.9
So 0.9 should be three standard deviations from mean.
The requi...

3*Standard deviation = 0.9
0.9
= 0.3
3
Standard deviation
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3*Standard deviation = 0.9 0.9 = 0.3 3 Standard deviation

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