I make shafts that are used in aircraft engines. Each shaft I make has a diamete

Question

I make shafts that are used in aircraft engines. Each shaft I make has a diameter that is a normally distributed random variable with a mean of 2 cm and a standard deviation of 0.004 cm. The FAA inspects every shaft and will reject a shaft whose diameter falls outside of the range 2 ± .006 cm. what proportion of my shafts get rejected? With respect to the previous problem, the FAA permits me to re-mill shafts whose diamters falls between 2.006 cm and 2.012 cm. What percentage of the shafts I produce may be re-milled?

Explanation / Answer

1)proportion of shafts rejected =1-Proportion accepted =1-P(2-0.006<X<2+0.006)

=1-P(-0.006/0.004<Z<0.006/0.004)=1-P(-1.5<Z<1.5)=0.9332-0.0668 =0.8664

2)

% of the shafts to be remillled =P(2.006<X<2.012)=P((2.006-2)/0.004<Z<(2.012-2)/0.004)=P(1.5<Z<3)

=0.9987-0.9332 =0.0655 ~ 6.55%

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