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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Andrea

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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}

Substitutek = 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

a. To find the probability that exactly 10 customers make purchases in a sample of 20, we can use the binomial probability formula:

Substitute

Calculating this gives:

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