According to the college registrar's office, 55% of students enrolled in an introductory statistics class this semester are freshmen, 25% are sophomores, 10% are juniors, and 10% are seniors. You want to determine the probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen. What is the probability of success?

Question

Mathematics

Nathanial

12 October, 16:27

According to the college registrar's office, 55% of students enrolled in an introductory statistics class this semester are freshmen, 25% are sophomores, 10% are juniors, and 10% are seniors. You want to determine the probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen. What is the probability of success?

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Litzy Mclaughlin · Answer 1

The probability of success is 0.276.

Step-by-step explanation:

since 55% of the students are enrolled in an introductory statistics class this semester are freshmen. the probabilities of exactly 2 freshmen is statistically independent, meaning we gonna use the binomial distribution.

In the binomial distribution:

n = 5, p = 0.55, x = 0, 1, 2, 3, 4, 5.

Probability that in a random sample of five students enrolled in introductory statistics this semester, exactly two are freshmen is:

P (X = 2) = [5!/2! (5 - 2) !] * (0.55) ^ (2) * (0.45) ^3

= 0.2756

Therefore, The probability of success is 0.276.