Question

A factory has a machine that makes steel rods. The length of the rods that the machine makes feet. Find the rod length rmal distribution curve with a mean of 11. 5 feet and a standard deviation of 03 The factory manager does not want to use the rods from the bottom 20% and the top 15%. S the manager will be using as the basis for separating the rods

Answer 1

The range for the rod will be  11.218  - 11.812 feet

Given,

A factory has a machine that makes steel rods. The length of the rods that the machine makes feet.

Mean, μ = 11.5 feet

Standard deviation, σ = 0.3

The factory manager does not want to use the rods from the bottom 20% and the top 15%.

We have to find the length of the rods that the machine makes follows a normal distribution curve.

Here,

The factory manager doesn't want percentile 0-20 and percentile 85-100.

Here,

We have 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

Therefore,

The range for the rod will be  11.218  - 11.812 feet

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