Check My World eBook Motorola used the normal distribution to determine the prob
ID: 3060122 • Letter: C
Question
Check My World eBook 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 15 ounces. a. The process standard deviation is 0.10, and the process control is set at plus or minus 1.25 standard deviations. Units with weights less than 14.875 or greater than 15.125 ounces will be dassified 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 (round to the nearest whole number)? b. Through process design improvements, the process standard deviation can be reduced to 0.08. Assume the process control remains the same, with weights less than 14.875 or greater than 15.125 ounces being classified as defects. what is the probability of a defect (round to 4 decimals; if necessary)? In a production run of 1000 parts, how many defects would be found (to the nearest whole number)? c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard deviations from the mean? - Select your answer - Check My Work 0 Iron Key 4 Quarte 12 of 16 -Explanation / Answer
Solution:- Given mean = 15 sd = 1.0
a) Probability of a defect = 1 - P(14.875 < X < 15.125)
= 1 - P(-1.25 < Z < 1.25)
= 1 - 0.7888
= 0.2112
=> in a production runs of 1000 parts,number of defectd = 1000*0.2112 = 211.2 = 211
b) sd = 0.08
probability of a defect = 1 - P((14.875 - 15)/0.08 < Z < (15.125 - 15)/0.08)
= 1 - P(-1.5625 < Z < 1.5625)
= 1 - 0.8812
= 0.1188
=> => in a production runs of 1000 parts,number of defectd = 1000*0.1188 = 118.8 = 119
c) advantage of reducing process variation is that probability of defect item is decreased.