Question

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 14 ounces.

The process standard deviation is 0.2, and the process control is set at plus or minus 0.5 standard deviation. Units with weights less than 13.9 or greater than 14.1 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)?


In a production run of 1000 parts, how many defects would be found (to 0 decimals)?

Through process design improvements, the process standard deviation can be reduced to 0.05. Assume the process control remains the same, with weights less than 13.9 or greater than 14.1 ounces being classified as defects. What is the probability of a defect (rounded to 4 decimals; getting the exact answer, although not necessary, will require Excel)?


In a production run of 1000 parts, how many defects would be found (to 0 decimals)?

What is the advantage of reducing process variation? SELECT A,B OR C

A.it can substantially reduce the number of defects

B.it may slightly reduce the number of defects

C.it has no effect

PLEASE SHOW YOUR WORK

Answer 1

Mean=14

a) Std= 0.2

The probability of defects= 1- P(Non defects)= 1- 0.3829= 0.6171

b) n= 1000, E(x)= np= 1000* 0.6171= 617.1

c) Std= 0.05

The probability of a defecct= 1- 0.9545= 0.0455

n= 1000, E(X)= np= 1000* 0.0455= 45.5

d) A.it can substantially reduce the number of defects, reduced defect rate from 617..1 to 45.5.