An efficiency expert has been hired by the Klondike Manufacturing Company to mon

Question

An efficiency expert has been hired by the Klondike Manufacturing Company to monitor the time required by the chassis assembly station of the transistor radio division to complete its assigned task. The results indicate that the time required for the station to produce the chassis and send it along to the next station is normally distributed with a mean of 16 minutes and a standard deviation of 2 minutes.

a)What is the probability that the station will complete its task in less than 18.5 minutes?
b) What is the probability that the station does as well as the optimal efficiency time of 14.2 minutes or less?
c)The probability is .1179 that the required task time will be under a certain value; find this value.

Explanation / Answer

a) probability that the station will complete its task in less than 18.5 minutes=P(X<18.5)=P(Z<(18.5-16)/2)

=P(Z<1.25)=0.8944

b)probability that the station does as well as the optimal efficiency time of 14.2 minutes or less

=P(X<14.2)=P(Z<-0.9)=0.1841

c)for 0.1179 probability ; z=-1.1856

hence corresponding value =mean +z*std deviation=16-1.1856*2=13.63 minute

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