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?
271
likes1353 views
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?
Andrea
4.586 Answers
Let's denote the probability of a customer making a purchase as p = 0.25 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 p = 0.25
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:
Frequently asked questions (FAQs)
What is the equation of a line with a slope of 3 and passing through the point (2,5)?
+
What is the length of the altitude drawn from vertex A in a triangle ABC, given AC = 10 cm, BC = 12 cm, and AB = 8 cm?
+
What is the radian measure of an angle subtended by an arc of length 3 cm on a circle with radius 2 cm?
+
New questions in Mathematics