To estimate the man height of male students on yoru campus, you will measure an

Question

To estimate the man height of male students on yoru campus, you will measure an SRS of students. You know from goverment data that hights of youn men are approximately Normal with standard devation about 2.8 inches. You want your sample mean x-bar to estimate with an erro of no more than one-half inch in either direction. a. What standard devaition must x-bar have so that 99.7% of all samples give an x-bar within one-half inch of (Use the 68-95-99.7 rule) b. How large an SRS do you need to reduce the standard devation of xbar to the value you found in part (a)? To estimate the man height of male students on yoru campus, you will measure an SRS of students. You know from goverment data that hights of youn men are approximately Normal with standard devation about 2.8 inches. You want your sample mean x-bar to estimate with an erro of no more than one-half inch in either direction. a. What standard devaition must x-bar have so that 99.7% of all samples give an x-bar within one-half inch of (Use the 68-95-99.7 rule) b. How large an SRS do you need to reduce the standard devation of xbar to the value you found in part (a)?

Explanation / Answer

Step 1: Define terms.

At = 0.003 z1-/2 = 3

= Standard deviation = 2.8

= error = 0.5

Step 2: Find the required sample size.

n = (z1-/2/)2

    = (3 * 2.8 / 0.5)2 = 282.4 =283

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