At Ersatz University, the graduating class of 480 includes 96 guest students from Latvia. A sample of 10 students is selected at random to attend a dinner with the Board of Governors. Use the binomial model to obtain the approximate hypergeometric probability that the sample contains at least three Latvian students.
A).3222
B).1209
C).8791
D).6778

Question

Quizplus · Accepted Answer

The hypergeometric probability is given by:P(X = k) = (C(K, k) * C(N-K, n-k)) / C(N, n)where:N is the total number of students in the graduating class (480)K is the number of Latvian students in the graduating class (96)n is the number of students in the sample (10)k is the number of Latvian students in the sampleTo find the approximate hypergeometric probability that the sample contains at least three Latvian students, we need to sum the probabilities for k = 3, 4, ..., 10.Using a calculator, we get:P(X >= 3) = 0.3222Therefore, the approximate hypergeometric probability that the sample contains at least three Latvian students is 0.3222.

At Ersatz University, the Graduating Class of 480 Includes 96