If the mean bone density test score is found for 16 randomly selected subjects,

Question

If the mean bone density test score is found for 16 randomly selected subjects, find the jrobabflity that the mean is greater than 0.27. k Door Peephole standing eye heights of women are normally distributed with a mean of W mm^^a standard deviation of 63 mm (based on anthropometric survey data flora Gordon, Churchill, et al.). a. A door peephole is placed at a height that is uncomfortable for women with staniiijig eye heights greater than 1605 mm. What percent uf women will find thai height uncomfortable? b. In selecting the height of a door peephole, the architect want* Its bright to be suitable for the highest 99% of standing eye heights ol women. What standing eye height af women the highe* 99% of standing ey>> heijjlus tram the lowest 1%?

Explanation / Answer

a. Find z score to obtain the required percentage of women who find the height uncomfortable.

Xi=1605mm, Xbar=1516mm and Sigma=63mm

Substitute the values in following equation.

z=(Xi-Xbar)/sigma=(1605-1516)63=1.41

Now look at z table to find the area corresponding to z score.0.9207 (Ans)

b. Here, z=0.99, find Xi using the z statistic formula.

0.99=(Xi-1516)/63

Xi=1578.37 (Ans)

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