Problem 196SE

Refer to Exercise 3.195. The cost of repairing the imperfections in the weave is $10 per imperfection. Find the mean and standard deviation of the repair cost for an 8-square-yard bolt of the textile.

Reference

The number of imperfections in the weave of a certain textile has a Poisson distribution with a mean of 4 per square yard. Find the probability that a

a 1-square-yard sample will contain at least one imperfection.

b 3-square-yard sample will contain at least one imperfection.

Solution 196SE

Step1 of 2:

We have the cost of repairing the imperfections in the weave is $10 per imperfection.

We need to find the mean and standard deviation of the repair cost for an 8-square-yard bolt of the textile.

Step2 of 2:

From Exercise 3.195 we have

Here they have given 8 square yard bolt of the textile.

Now,

The cost is the product of the cost per imperfections and the number of imperfections:

We know that mean and variance of poisson distribution and it is given as:

Mean of Y is given by:

= 320

Therefore, Mean of Y is 320.

Variance of Y is given by:

= 3200

Therefore, Variance of Y is 3200.

Now,

Standard deviation of Y is given by:

= 56.5685

Therefore, Standard deviation of Y is 56.5685.