Question

An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.76 inch. The lower and upper specification limits under which the ball bearings can operate are 0.75 inch and 0.77 ?inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally?distributed, with a mean of 0.764 inch and a standard deviation of 0.007 inch. Complete parts? (a) through? (e) below.

a. What is the probability that a ball bearing is between the target and the actual? mean?

?(Round to four decimal places as? needed.)

b. What is the probability that a ball bearing is between the lower specification limit and the? target?

?(Round to four decimal places as? needed.)

c. What is the probability that a ball bearing is above the upper specification? limit?

?(Round to four decimal places as? needed.)

d. What is the probability that a ball bearing is below the lower specification? limit?

?(Round to four decimal places as? needed.)

e. Of all the ball? bearings, 91% of the diameters are greater than what? value? (in inches)

(Round to three decimal places as? needed.)

Answer 1

a)

probability that a ball bearing is between the target and the actual? mean

=P(0.76<X<0.764)=P((0.76-0.764)/0.007<Z<(0.764-0.76)/0.007)=P(-0.57<Z<0)=0.5-0.2843=0.2157

b)

P(0.75<X<0.76)=P(-2<Z<-0.57)=0.2843-0.0228 =0.2615

c)

P(X>0.77)=P(Z>0.86)=0.1949

d)

P(X<0.75)=P(Z<-2)=0.0228

e)for top 91% values at 9th percentile ;critical z =-1.34

therfore corresoponding value =mean+z*std deviation =0.764-1.34*0.007=0.755 inches