The probability that a randomly selected individual in a certain community has made an online purchase is 0.41 . Suppose that a sample of 13 people from the community is selected, what is the probability that at most 3 of them has made an online purchase? Write only a number as your answer. Round to 2 decimal places (for example 0.24). Do not write as a percentage.

0.15

Step-by-step explanation:

What we can use to solve this problem is the Bernoulli approximation of the Binomial distribution.

When we say at most 3, it means 0 or 1 or 2 or 3 people out of the 13 made the purchase

Mathematically, the Bernoulli approximation is applied as follows

P(X = n) = nCr p^r q^n-r

let p = probability of making online purchase = 0.41

while q = 1-p = 1-0.41 = 0.59 which is the probability of not making an online purchase.

Mathematically for each of the approximations up to 3, we have ;

13C0 P^0 q^13 + 13C1 P^1 q^12 + 13C2 P^2 q^11 + 13C3 P^3 q^10

Making substitutions, we have

{1 * 0.41^0 * 0.59^13} + {13 * 0.41^1 * 0.59^12} + {78 * 0.41^2 * 0.59^11} + {286 * 0.41^3 * 0.59^10}

= 0.150820944904 which is 0.15 to 2 decimal places

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.