A plastic casing for a magnetic disk is composed of two halves. The thickness of each half is normally distributed with a mean of 2 millimeters, and a standard deviation of 0.1 millimeter and the halves are independent.

(a) Determine the mean and standard deviation of the total thickness of the two halves.

(b) What is the probability that the total thickness exceeds 4.3 millimeters?

Answer

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(a)

We have given a plastic casing for a magnetic disk is composed of two halves.

The thickness of each half is normally distributed with a mean of and a standard deviation of and the halves are independent.

We are asked to find the mean and standard deviation of the total thickness of the two halves.

Let denote the total thickness.

Then, ……….(1)

If are independent, normal random variables with

Is a normal random variable with

…….(2)

………(3)

Hence the mean and standard deviation of the total thickness of the two halves using equation

……….(4)

Compare equation (1) and (4), we get

Hence the mean and standard deviation of the total thickness of the two halves is respectively.