A technician assembles electronic devices. The mean time required to assemble a

Question

A technician assembles electronic devices. The mean time required to assemble a device is 15.0 minutes, with a standard deviation of 3.0 minutes. The devices are all the same, and the time required to assemble one is independent of the time to assemble any other. What is the expected value of the time needed to produce 25 devices? What is the standard deviation of this quantity? The technician can go home at the end of his 6-hour shift or when he's completed 25 devices, whichever comes first. Use the central limit theorem to estimate the probability that he goes home early.

Explanation / Answer

Q.4(a) Mean time to assembke a device = 15.0 minutes

Std. dev = 3.0 minutes

so variance = 9.0

Expected value of the time needed to produce 25 devices = 15 * 25 = 375 minutes

cumulative Variance of the time needed to produce 25 devices = 9.0 * 25 = 225.0 minutes2

std. dev . of the time needed to produce 25 devices = sqrt(variance) = 15.0 min

(b) Eigher end of his 6 - hour shift ( = 360 minutes)or when he's completed 25 devices which have expected time 375 minutes with std. deviation of 15 minutes.

so here we have calculate the probability that he' s completed 25 devices before 360 minutes so he can go early.

so P( t <= 360, 375; 15)

z - value = ( 360 - 375)/15 = -1 so p - value = 0.1587

P( t <= 360, 375; 15) = 0.1587

so, it is 15. 87% probable that he can go home early before this 6- hour shift.

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