Respuesta :
Using the binomial distribution, it is found that there is a 0.957 = 95.7% probability that he sells less than 3 cars.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- The probability a car salesman sells a car to a customer is 0.05, hence p = 0.05.
- The salesmen sees 16 customers in a week, hence n = 16.
The probability he sells less than 3 cars is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{16,0}.(0.05)^{0}.(0.95)^{16} = 0.4401[/tex]
[tex]P(X = 1) = C_{16,1}.(0.05)^{1}.(0.95)^{15} = 0.3706[/tex]
[tex]P(X = 2) = C_{16,2}.(0.05)^{2}.(0.95)^{14} = 0.1463[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4401 + 0.3706 + 0.1463 = 0.957.
0.957 = 95.7% probability that he sells less than 3 cars.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
