Question

Suppose the probability of selling a white car to a buyer older than 50 is.8 and it is .4 if the buyer is younger than 50. Suppose half of all customers are older than 50. (a) What is the probability of an arbitrary customer purchasing a white car? (b) Suppose 10 customers are currently in the showroom. What are the mean number of white cars purchased and what is the variance (c) LetXthe number white cars purchased by the 10 customers, then P(X > 5)- (d) P(x 2 5)-

Answer 1

a)P(arbitrary customer purchasing a white car) =P(older than 50 and buys a white car+younger than 50 and buys a white car) =0.5*0.8+0.5*0.4=0.6

b)

for binomial distirbution parameter p=0.6 and n=10

mean $\mu$ =np =10*0.6 =6

and varaince= $\sigma$ ² =np(1-p)=10*0.6*(1-0.6)=2.4

c)P(X>5) =P(X=6)+P(X=7)+...+P(X=10) = $\sum_{x=6}^{10}\binom{10}{x}(0.6)^{x}(0.4)^{10-x}$ =0.6331

d)P(X>=5) =P(X=5)+P(X=6)+P(X=7)+...+P(X=10) = $\sum_{x=5}^{10}\binom{10}{x}(0.6)^{x}(0.4)^{10-x}$ =0.8338