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."
Accepted Solution
A:
Answer:11.218 - 11.812 feetStep-by-step 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