(1 point) To estimate the mean height μμ 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 x⎯⎯⎯x¯ to estimate μμ with an error of no more than one-half inch in either direction. (a) What standard deviation must x⎯⎯⎯x¯ have so that 99.7% of all samples give an x⎯⎯⎯x¯ within one-half inch of μμ? (Use the 68-95-99.7 rule.) (b) How large an SRS do you need to reduce the standard deviation of x⎯⎯⎯x¯ to the value you found in part(a)?
Added by Jasmine H.
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Given that 1 standard deviation = 1/6 inch, we can calculate the standard deviation needed as follows: Standard deviation = 1/6 = 0.1667 inches 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)?
Dominador T.
(1 point) 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 the heights of young men are approximately Normal with standard deviation about 2.8 inches. You want your sample mean x to estimate μ with an error of no more than one-half inch in either direction. (a) What standard deviation must x have so that 95% of all samples give an x 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 x to the value you found in part(a)?
Lucas F.
At a large university, the heights of male students who are interscholastic athletes is approximately normally distributed with a mean of 74.3 inches and a standard deviation of 3.5 inches. The heights of male students who do not play interscholastic sports is approximately normally distributed with a mean of 70.3 inches and a standard deviation of 3.2 inches. You select a simple random sample (SRS) of 10 interscholastic athletes and 12 non-interscholastic athletes. A) Find the mean of the sampling distribution. B) Find the standard deviation to the nearest hundredth of the sampling distribution.
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