Born year is 1995.
Present year is 2017.
Difference between present year and born year is = 2017 - 1995
= 22 years.
So my present age is = 22 year.
Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that more than 7 will make a purchase.
<h3>What is the binomial distribution formula?</h3>
The formula is:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
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:
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 8) = C_{12,8}.(0.4)^{8}.(0.6)^{4} = 0.042](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20C_%7B12%2C8%7D.%280.4%29%5E%7B8%7D.%280.6%29%5E%7B4%7D%20%3D%200.042)
![P(X = 9) = C_{12,9}.(0.4)^{9}.(0.6)^{3} = 0.012](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B12%2C9%7D.%280.4%29%5E%7B9%7D.%280.6%29%5E%7B3%7D%20%3D%200.012)
![P(X = 10) = C_{12,10}.(0.4)^{10}.(0.6)^{2} = 0.02](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%3D%20C_%7B12%2C10%7D.%280.4%29%5E%7B10%7D.%280.6%29%5E%7B2%7D%20%3D%200.02)
![P(X = 11) = C_{12,11}.(0.4)^{11}.(0.6)^{1} \approx 0](https://tex.z-dn.net/?f=P%28X%20%3D%2011%29%20%3D%20C_%7B12%2C11%7D.%280.4%29%5E%7B11%7D.%280.6%29%5E%7B1%7D%20%5Capprox%200)
![P(X = 12) = C_{12,12}.(0.4)^{12}.(0.6)^{0} \approx 0](https://tex.z-dn.net/?f=P%28X%20%3D%2012%29%20%3D%20C_%7B12%2C12%7D.%280.4%29%5E%7B12%7D.%280.6%29%5E%7B0%7D%20%5Capprox%200)
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 brainly.com/question/24863377
I think 45, because for women, if you do 15 * 1 = 15. For men, you would do 15* 3 = 45.