# 請問統計問題（ normal distribution ）

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 is designed to produce items with a weight of 10 ounces and that the process mean is 10.

Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situations.

a.The process standard deviation is 0.15 ,and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

b.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 9.85 or greater than 10.15 ounces will be classified as defects.

c.What is the advantage of reducing process variation and setting process control limits at a greater number of standard deviations form the mean?

Rating

a.

P(x<9.85 , 10.15<x)標準化

= P[Z<(9.85-10)/0.15 , (10.15-10)/0.15)<Z]

= P(Z<-1 , 1<Z) = P(|Z|>1) = 0.1578*2 = 0.3156

b.

P(x<9.85 , 10.15<x)標準化

= P[Z<(9.85-10)/0.05 , (10.15-10)/0.05)<Z]

= P(|Z|>3) = 0.0013*2 = 0.0026

c.

不太懂題目在講什麼，大概是說哪一種標準差比較好

對於廠商來講，不良率愈小愈好

所以應該是0.05的標準差會比較好

Source(s): me