Question

Hi!! please help with my statistics homework. I have no clue..

"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 lengths the manager will be using as the basis for separating the rods."

Answer 1

11.218 - 11.812 feet

Explanation:

The factory manager does not want to use the rods from the bottom 20% and the top 15%. In other words, the factory manager doesn't want percentile 0-20 and percentile 85-100.

To solve this question, you need to know the z score of percentile 20 and 85.

Z-score of percentile 20 is -0.94, then the calculation will be :

x= 11.5 feet+ 0.3 feet* z-score

x= 11.5 feet+ 0.3 feet* (-0.94)

x= 11.5 feet- 0.282 feet

x= 11.218 feet

Z-score of percentile 85 is +1.04 then the calculation will be :

x= 11.5 feet+ 0.3 feet* z-score

x= 11.5 feet+ 0.3 feet* 1.04

x= 11.5 feet+ 0.312 feet

x= 11.812 feet

The range for the rod will be 11.218 - 11.812 feet