Motorola used the normal distribution to determine the probability of defects an

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 8 ounces. a. The process standard deviation is 0.20, and the process control is set at plus or minus 0.75 standard deviation, Units with weights less than 7.5 or greater than 8.15 ounces will be classified as defects, What is the probability of a defect (to 4 decimals)? In a production run of 100U 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 0.07. Assume the process control remains the same, with weights less than 7.85 or greater than 8.13 ounces being dassified 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)?

Explanation / Answer

a) here Probability of defect =P(X<7.85 or X>8.15)=1-P(7.85<X<8.15)=1-P((7.85-8)/0.2<Z<(8.15-8)/0.2)

=1-P(-0.75<Z<0.75)=1-(0.7734-0.2266) =0.4533

b)approximate number of defects =np=1000*0.4533 =~453

c)Probability of defect =P(X<7.85 or X>8.15)=1-P(7.85<X<8.15)=1-P((7.85-8)/0.07<Z<(8.15-8)/0.07)

=1-P(-2.1429<Z<2.1429)=1-(0.9839-0.0161) =0.0321

d)defects =np =1000*0.0321=~32

please revert for any clarification required

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