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Nuts and bolts are manufactured independently. The inner radius of nuts are normally distributed with mean...

Nuts and bolts are manufactured independently. The inner radius of nuts are normally distributed with mean 1.0 cm and standard deviation 0.015 cm, and the outer radius of bolts are normally distributed with mean 0.95 cm and standard deviation 0.015 cm.

Provided that bolt radius is within 0.1 cm of the nut radius, the nut and bolt will fit.

What is the probability of a random nut and bolt fitting?

Math   Statistics-And-Probability   
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Answer #1

LET X IS THEN INNER RADIUS OF NUTS

& Y IS OUTER RADIUS OF BOLTS

SINCE X & Y ARE INDEPENDENT

BY ADDITIVE PROPERTY OF NORMAL DISTRIBUTION ,

Provided that bolt radius is within 0.1 cm of the nut radius, the nut and bolt will fit.

That means , We have to find probability of

  

  

Where Z IS STANDARD NORMAL DISTRIBUTION .

  

Probability of a random nut and bolt fitting is 0.9086

  

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