Question

Answer the following questions.

Question 2. A store manager claims that thirty percent of customers who enter the store will make a purchase. Suppose six customers enter the and that these customers make independent purchase decisions a. What is the random variable of interest? b. What is the probability that exactly five customers make a purchase? c. What is the probability that at least three customers make a purchase? d. What is the probability that two or fewer customers make a purchase? e. What is the probability that between three and five customers make a purchase? f. How many customers would be expected to buy if 3000 customers visit the store in a given day?

Please arrange the answers in a direct and easier to understand fashion. For example:

1. Example Answer

2. Example Answer 2

3. Ex Ans...

etc.

Answer 1

30% of customers will make purchase p = 0.3 six customers enter n = 6 a) X rightarrow random variable number of customer will make purchase x rightarrow binomial distribution with n = 6 p = 0.3 b) p(exactly 5 customers) = p(X = 5) p(X = x) = n_c_x p^x (1 - p)^n - x p(X = 5) = 6_c_5 (0.3)^5 (0.7)^1 = 6(0.3)^5 (0.7) = 0.0102 c) p(at least 3 customers) = p(X > , 3) = p(X = 3) + p(X = 4) + p(X = 6) + p(X = 6) 6_c_3 (0.3)^3 + 6_c_4 (0.3)^4 (0.7)^2 + 6_c_5 (0.3)^5 (0.7) + 6_c_6 (0.3)^6 (0.7) = 0.2557 \r\n d) P(two or fewer) = P(X lessthanorequalto 2) = P(X = 0) + P(X = 1) + P(x = 2) = 6_c_0 (0.3)^0 (0.7)^0