Answer to Question #196111 in Statistics and Probability for Betty

Question

A car dealership has both Electric and Internal Combustion Engine (ICE) vehicles available for sale. 30% of customers looking to purchase a new car are interested in Electric vehicles, while the rest want ICE vehicles. On a particular day, the dealership had 17 people coming in to purchase a new car.

a) What is the mean value and the standard deviation of the number of people who were interested in purchasing an Electric vehicle?

b) What is the probability that the number of people who are interested in an Electric vehicle is more than two standard deviations away from the mean value?

c) The dealership only has 9 Electric vehicles and 13 ICE vehicles in stock. If the 17 people are served on a first-come-first-serve basis, what is the probability that all of them will be able to purchase the type of vehicle they want?

Answer 1

We have given that,

p = 0.3

q = 0.7

n = 17

a.) Mean $= np = 17 \times 0.3 = 5.1$

Standard Deviation $= \sqrt{17 \times 0.3 \times 0.7} = 1.88$

b.) The probability that the number of people who are interested in an Electric vehicle is more than two standard deviations away from the mean value

$=P(X<\mu-2\sigma)+P(X>\mu+2\sigma)$

$= P(Z<-2)+ P(Z>-2)$

$= 0.0228+0.0228 = 0.0456$

c.) The probability that all of them will be able to purchase the type of vehicle they want

$= \dfrac{^{17}C_{17}}{^{22}C_{17}}$