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)