q12 Digital Industries uses statistical quality control to monitor the productio

Question

q12

Digital Industries uses statistical quality control to monitor the production process during the manufacture of memory chips. The electrical usage across a conducting zone for a memory chip is normally distributed with a mean of 10.05 microvolts and a standard deviation of 0.92 microvolts. A quality control manager randomly samples 4 memory chips. What is the probability that the sample mean is between 8.67 and 11.43 microvolts?
(a) 0.8664
(b) 0.4987
(c) 0.9974
(d) 0.9332
(e) cannot be determined as the sample size is too small (ie. n < 30)

Explanation / Answer

Sol:

mean=10.05

pop sd=0.92

n=4

sampel sd=s=pop sd/sqrt(n)=0.92/sqrt(4)=0.92/2=0.46

P(8.67<Xbar<11.43)

P(Xbar<11.43)-P(Xbar<8.67)

Rcode is

pnorm(11.43,mean=10.05,sd=0.46)-pnorm(8.67,mean=10.05,sd=0.46)

=0.9973002

ANSWER:

OPTION C 0.9974

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