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). \\vspace {4cm} b) [3 point] calculate the expected value and standard deviation of $X$ . \\vspace{3cm} c) [3 points] what is the probability that all $20$ airbags functioned properly? \\vspace {2cm} d) [2 points] what is the probability that airbags in the first two cars did not function properly, but all the other ones did? \\vspace {3cm} e) [2 points] Let $2$ denote the number of airbags that did function properly. what is the distribution of $Z$? As before, please make sure to give the name of the distribution family and the associated parameters