College

To estimate the mean score μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of a Simple Random Sample (SRS) of students. From published information, you know that the scores are approximately Normal with a standard deviation of about 6.6. You want your sample mean \(\overline{x}\) to estimate μ with an error of no more than 1.4 points in either direction.

What standard deviation (±0.0001) must \(\overline{x}\) have so that 99.7% of all samples give an \(\overline{x}\) within 1.4 points of μ?

Answer :

Answer:

standard deviation = ±0.4667

Step-by-step explanation:

In Normal distribution, approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.

Therefore, for a confidence interval of 99.7% the standard deviation of the x¯ must be 3 standard deviations from the mean,

3σ = ±1.4

σ = ±1.4/3

σ = ±0.4667

Therefore, 0.4667 is the standard deviation that x¯ must have so that 99.7% of all samples give an x¯ within 1.4 point of μ.

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