In Exercise 5-31, the monthly demand for MMR vaccine was assumed to be approximately normally distributed with a mean and standard deviation of 1.1 and 0.3 million doses, respectively. Suppose that the demands for different months are independent, and let Z denote the demand for a year (in millions of does). Determine the following:

Step 1 of 5</p>

Given that the monthly demand of MMr follows the normal distribution with mean 1.1 and standard deviation 0.3

Let X denote the monthly demand

Here

Let Z denote the yearly demand

Then Z=12X

Step 2 of 5</p>

a) We have to find mean, variance and the distribution of Z

Now mean(Z)=

=

=12(1.1)

=13.2

Variance (Z)=

=144(0.3)2

=12.96

Standard deviation (Z)=

=3.6

Here X follows the normal distribution

then Z=12X also follows the normal distribution

Step 3 of 5</p>

b) We have to find

Now

=

=0.5

Hence =0.5