I only need the answer for 2 Ignore 1 it is only there to

1. You have been hired to fix the problems at Ron Burgundy?s hole making factory. The holes location is .500 .005 in the Y-axis. His factory currently uses a combination square and drill press to make the holes. You measure a sample of parts and find the mean to be .510 and the standard deviation to be .011. What is the percentage of parts that are acceptable and what is the percentage of part that are rejectable? 2. Based on your recommendation the factory floor decides to use a fixture and a mill to make the holes in the parts. The new mean is .501 and the standard deviation is .002. What arc the new percentages for acceptable and rejectable?

Solution

0.500-0.005 = 0.495
0.500+0.005 = 0.505

population mean,u = 0.501
standard deviation,sigma = 0.002

P( 0.495 <X< 0.505 )
= P( ((0.495-0.501) / 0.002) <Z< ((0.505-0.501) / 0.002) )
= P( -3.00 <Z< 2.00 )
= P(Z<2) - P(Z<-3)
= P(Z<2) - (1 - P(Z<3))
= 0.9772 - ( 1 - 0.9987)
= 0.9772 - 0.0013
= 0.9759

percentage of parts that are acceptable = 97.59%
percentage of parts that are rejectable = 100-97.59 = 2.41%