A ceramic multilayer capacitor is rated at 100 microFarad with a tolerance of +

Question

A ceramic multilayer capacitor is rated at 100 microFarad with a tolerance of + OR - 20% . The manufacturer's internal specification is that the capacitance of capacitors should be within the interval [90,110] microFarad. Assume that the capacitances have a normal distribution. (a) Suppose the process mean is 104.0 and the standard deviation is 4.1. What proportion of capacitors will lie outside the internal specification? How many parts per million would be outside the tolerance? (b) The manufacturer adjusts the process so that the mean is 100.0. What does the standard deviation need to be reduced to so that 0.997 of production is within the internal specification? (c) Suppose the standard deviation is reduced to the value you calculate in (b), but the mean remains at 104.0. What proportion of capacitors would now lie outside the internal specification?

Explanation / Answer

a. The process mean is 104.0 and sd=4.1

P(90<X<110)=P(90-104/4.1<(X-104)/4.1<(110-104)/4.1)=P(-3.4146<Z<1.4634)=0.928321-0.00032=0.928001

Hence, 1-0.928001=0.072 proportion of capacitors will lie outside the internal specification.

b. Let the sd be s

P(-14/s<Z<)

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