A particular manufacturing design reqires a shaft with a diameter between 23.90

Question

A particular manufacturing design reqires a shaft with a diameter between 23.90 mm and 24.015 mm. The manufacturing process yeilds shafts with diameters normally distributed, with a mean of 24.002 and a standard deviation of 0.006 mm. Complete parts (a) through (c).                                                       a. the proportion of shafts with a diameter between 23.90 mm and 24.90 mm? (b) what is the probability that a          shaft is acceptable ? (c) is what the diameter that wilk be exceeded by only 1% of the shafts?                                        

Explanation / Answer

a) proportion of shafts with a diameter between 23.90 mm and 24.90 mm=P(23.90<X<24.015)

=P((23.9-24.002)/0.006<Z<(24.90-24.002)/0.006)=P(-17<Z<149.6667)=1-0=1

b)probability that a          shaft is acceptable=P(23.90<X<24.015)=P(-17<Z<2.1667)=0.9849-0=0.9849

c)for top 1% ; at 99th percentile z=2.3263

hence diameter =mean +z*std deviation=24.016

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