Answer to Question #291842 in Statistics and Probability for Sky

Question

If the diameters of ball bearings are normally distributed with mean 0.6140 inches and standard deviation 0.0025 inches, determine the percentage of ball bearings with diameters, (a) between 0.610 and 0.618 inches inclusive (b) greater than 0.617 inches (c) Less than 0.608 inches.

Answer 1

Solution:

$z =\dfrac{x-\mu}{\sigma}= (x-0.6140)/0.0025$

a)P(0.610<x<0.618)=P(-1.6<z<1.6)

=F(1.6)-F(-1.6))

=0.94508-0.0548

=0.8904

b)P(x>0.617)=P(z>1.2)

=1-F(z=1.2)

=1-0.8849

=0.1151

c)P(x<0.608)=P(z<-2.4)

=F(z=2.4)

=0.008