7. a factory has a machine that makes steel rods. The length of the rods that the machine makes follows a normal distribution curve with a mean of 11.5 feet and a standard deviation of 0.3 feet. The factory manager does not want to use the rods from the bottom 20% and the top 15%. Find the rod length the manager will be using as the basis for separating the rods.

Question

a). 11.56 and 11.86
b). 11.55 and 11.74
c). 11.19 and 11.75
d). 11.25 and 11.81

Answer 1

use a z-score table to find the lengths represented by bottom 20% and the top 15% of the population

the top is ≈ 1.04 s.d. above the mean

the bottom is ≈ 0.84 s.d. below the mean

Answer 2

Z = (score-mean)/SD

1.04 = (score-11.5)/.3

Solve for top score, repeat process for bottom score.