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.

(a) What is the expected value of the time needed to produce 25 devices? What is the standard deviation of this quantity?

(b) 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

X - time required to assemble a device

E(X) = 15 ,sd (X) = 3

Y = X1+X2 + ... Xn

E(Y) = n*15 sd(Y) = 3*sqrt(n)

a) n= 25 ,

E(Y) = 25*15 = 375 min

sd(Y) = 3*sqrt(25) = 15

b) P(Y< 360)

Z =(Y - 375)/15

P(Z< (360-375)/15)

P(Z< -1)

=0.15869

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