Step 2 Find the expected value for the number of customers w

Step 2: Find the expected value for the number of customers who prefer Universal Life. Round your answer to two decimal places.

Solution

let X1 be the number of customers prefer Whole life,X2 be the number of customers prefer UNIVERSAL life,X3 be the number of customers prefer life annuties.

now it is said that 30% prefer whole life,20% prefer universal life,50% prefer life annuties.

total number of customers tabulated=n=230

so (X1,X2,X3) jointly follows a multinomial distribution with paramaters (n=230,p1=0.3,p2=0.2,p3=0.5)

with the marginal distributions as X1~Bin(n,p1) X2~Bin(n.p2)   X3~Bin(n,p3)

step 1. expected value for the number of customers who prefer whole life is

E[X1]=np1=230*0.3=69 [answer]

step 2. expected value for the number of customers who prefer universal life is

E[X2]=np2=230*0.2=46 [answer]