15. A car manufacturing company is testing a new airbag system for their new model of car. It is known

that on average 1 in 100 airbags does not function properly in a simulated crash scenario. The new

system is installed on 20 cars of the new model and tested independently under similar simulated crash

scenarios. Let X denote the number of cars where the airbags failed to function properly.

a) [2 points] What probability distribution is appropriate to model the random variable X ? (justify your

answer, be sure to give the name of the distribution and the values of its parameters).

b) [3 point] Calculate the expected value and standard deviation of X .

c) [3 points] What is the probability that all 20 airbags functioned properly?

d) [2 points] What is the probability that airbags in the first two cars did not function properly, but all

the other ones did?