Question

4. Freebirds in IV receives N customers per day, where N is a random variable with mean 200
and standard deviation 40. The amount spent by each customer is normally distributed with
mean $15 and standard deviation $3. The amounts that customers spend are independent of
each other and independent of N. Find the mean and variance of the total amount spent at
Freebirds per day.

1. Freebirds in IV receives N customers per day, where N is a random variable with mean 200 and standard deviation 40. The amount spent by each customer is normally distributed with mean $15 and staudard deviation S3. The amounts that customers spend are independent of each other and independent of N. Find the mea and variauce of the total amount speut at Freebirds per day

Answer 1

here let total amount spend by N customers is Y and random amount spent by each customer is Xi;

Y =X1+X2+X3+...+Xn

therefore mean of total amount spent E(Y)=E(Y)=E(N)*E(X)=200*15=3000

and variance Var(Y)=E(N)*Var(X)+(E(X))²*Var(N)=200*9+(15)²*(40)² =361800