Problem 8SE

A certain type of plywood consists of five layers. The thicknesses of the layers are independent and normally distributed with mean 5mm and standard deviation 0.2 mm.

a. Find the mean thickness of the plywood.

b. Find the standard deviation of the thickness of the plywood.

c. Find the probability that the plywood is less than 24 mm thick.

Answer:

Step 1 of 3:

In this question we have asked to find the mean and standard deviation of the thickness of a piece of plywood which is composed of five layers.

Given data:

The thickness of layer has mean of 5 mm and standard deviation of 0.2 mm.

(a)

Let is the thickness of the five layers and we will consider thickness as a independent random variables.

Then total thickness of the layers can be written like this which is a special case of linear combination.

So we can write the mean of sum as follows

………….(1)

We have asked to find the mean thickness of the plywood.

So we can write equation 1 as ……………(2)

Put the value of mean into equation 2

= 25mm

Hence the mean thickness of the plywood is 25 mm.