To estimate the mean height μ of male students on your campus, you will measure an SRS of students. You know from government data that heights of young men are approximately normally distributed with a standard deviation of about 2.8 inches. You want your sample mean x-bar to estimate μ with an error of no more than one-half inch in either direction. (a) What standard deviation must x-bar have so that 99.7% of all samples give an x-bar within one-half inch of μ? (Use the 68-95-99.7 rule.) (b) How large of an SRS do you need to reduce the standard deviation of x-bar to the value you found in part (a)? Show your work.
Added by Rodrigo R.
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7% of all samples give an x-bar within one-half inch of μ, we can use the 68-95-99.7 rule to determine the standard deviation needed for x-bar. Since 99.7% falls within three standard deviations, we have 3 standard deviations = 1 inch. Therefore, the standard Show more…
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To estimate the mean height μ of male students on your campus, you will measure an SRS of students. You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. You want your sample mean x̄ to estimate μ with an error of no more than one-half inch in either direction. (a) What standard deviation must x̄ have so that 68% of all samples give an x̄ within one-half inch of μ? (Use the 68-95-99.7 rule.) (b) How large an SRS do you need to reduce the standard deviation of x̄ to the value you found in part(a)?
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