Question

In a particular retail clothing store, approximately 25% of potential customers who walk into the store make a purchase. In a random sample of 20 customers that walked into the store, ________________________________________ a. what is the probability that exactly 10 of the customers make purchases? b. what is the probability that at least 2 of the customers make purchases? c. how many of the customers are expected to make purchases? d. what is the standard deviation of the number of customers who make purchases?

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Answer to a math question In a particular retail clothing store, approximately 25% of potential customers who walk into the store make a purchase. In a random sample of 20 customers that walked into the store, ________________________________________ a. what is the probability that exactly 10 of the customers make purchases? b. what is the probability that at least 2 of the customers make purchases? c. how many of the customers are expected to make purchases? d. what is the standard deviation of the number of customers who make purchases?

Expert avatar
Andrea
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42 Answers
Let's denote the probability of a customer making a purchase as p = 0.25 and the number of trials as n = 20 .

a. To find the probability that exactly 10 customers make purchases in a sample of 20, we can use the binomial probability formula:
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}

Substitute k = 10 , n = 20 , and p = 0.25 into the formula:
P(X = 10) = \binom{20}{10} \cdot (0.25)^{10} \cdot (0.75)^{10}

Calculating this gives:
P(X=10)=\binom{20}{10}\cdot(0.25)^{10}\cdot(0.75)^{10}\approx0.0099



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