a quality control program on a automated assembly line monit

a quality control program on a automated assembly line monitors the number of boxes mishandled by being placed out of order or dropped off the line. The program assigns QC score of 1 for a box placed out of order and assigns a QC score of 3 for a box that is dropped

-Assume the number of out of order boxes has a mean of 5 and standard deviation of 2

-ASsume the number of dropped boxes has a mean of 2 and standard deviation of 1

A. Find the average QC score assigned by the program

B.Assume the number of dropped boxes is independednt of the number of out of order boxes. Find the variance of the QC score

Solution

Suppose that

X= number of out of order boxes

Y= number of dropped boxes

we are given that mean(x) =5

var(x) = 2^2 =4

mean (y) = 2

var(y)=1

thus E(QC Score) = E(x)+E(y)

= 5+2

=7

similarly var(x+y) = var(x) +var(y) (covariance term is zero because x and y are independent of each other)

= 4+1

=5