Question

You are selling your car. Potential customers will buy the car with probability p=0.05
Answer the following questions, rounding your answers to 4 digits.
1 a) Numerical
What is the probability that the 11th customer will buy the car?
1 b) Numerical
What is the probability that one of the first 11 customers will buy the car?
1 c) Numerical
What is the expected rank of the customers who will buy the car, E(X)?
1 d) Algebraic
Enter the formula of the quantile function 1/F(m) , the function solving x: F(x)=m. You can use any symbol for the variables.
1 e) Numerical
What is the 3rd quartile of the distribution?

Answer 1

1 a) Numerical
What is the probability that the 11th customer will buy the car?
geometric distribution
= (1-p)^(k-1) * p
= (0.95)^10 * 0.05
=

1 b) Numerical
What is the probability that one of the first 11 customers will buy the car?
= 1- P(none of them will buy)
= 1- 0.95^11
=

1 c) Numerical
What is the expected rank of the customers who will buy the car, E(X)?
E(X) = 1/p = 1/0.05 = 20

1 d) Algebraic
Enter the formula of the quantile function 1/F(m) , the function solving x: F(x)=m.

F(x) = 1- (1-p)^x

e)
0.75 = 1- 0.95^x
0.25 = 0.95^x
x = 27.0268
= 28