Respuesta :
Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that more than 7 will make a purchase.
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:
- There are 12 customers, hence n = 12.
- The probability of any of them making a purchase is of p = 0.4.
The probability that more than 7 will make a purchase is given by:
P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12).
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{12,8}.(0.4)^{8}.(0.6)^{4} = 0.042[/tex]
[tex]P(X = 9) = C_{12,9}.(0.4)^{9}.(0.6)^{3} = 0.012[/tex]
[tex]P(X = 10) = C_{12,10}.(0.4)^{10}.(0.6)^{2} = 0.02[/tex]
[tex]P(X = 11) = C_{12,11}.(0.4)^{11}.(0.6)^{1} \approx 0[/tex]
[tex]P(X = 12) = C_{12,12}.(0.4)^{12}.(0.6)^{0} \approx 0[/tex]
Then:
P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.042 + 0.012 + 0.02 + 0 + 0 = 0.056.
0.056 = 5.6% probability that more than 7 will make a purchase.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
