Question

Assume that any student has a 25% chance of getting into a certain college. Let the random variable X denote the number of students (from a total of 5 students who apply) who get into the school. For the following problems do not use calculator commands.

a. What are the parameters n and p for the distribution?

b. What is the expected number of students (out of the 5) who will be accepted to the school?

c. Find the standard deviation of X.

d. How many ways can you choose two out of these 5 students?

e. What is the probability that none of the students are accepted to the school?

f. What is the probability that more than two of the students are accepted to the school?

Answer 1

a) n = 5

p = 0.25

b) expected number = n * p = 5 * 0.25 = 1.25

c) standard deviation = sqrt(n * p * (1 - p)) = sqrt(5 * 0.25 * 0.75) = 0.97

d) Number of ways to choose two out of these 5 students = 5C2 = 5! / (2! * (5 - 2)!) = 10

e) P(none of the students are accepted to the school) = (1 - 0.25)⁵ = 0.2373

f) P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5)

                 = 5C3 * 0.25³ * 0.75² + 5C4 * 0.25⁴ * 0.75¹ + 5C5 * 0.25⁵ * 0.75⁰

                 = 0.1035