Question

A group of Martial Arts students is planning on participating in an upcoming demonstration. Six are students of Tae Kwon Do; seven are students of Shotokan Karate. Suppose that eight students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate students in that first demonstration.; X; X

a. There are no Shotokan Karate students.

b. There is one Shotokan Karate student.

c. There are two Shotokan Karate students.

d. There are three Shotokan Karate students.

Answer 1

The random variable X represents the number of Shotokan Karate students in the first demonstration. The expected number of Shotokan Karate students in the demonstration is around 4.

Step-by-step explanation:

The random variable X in this question represents the number of Shotokan Karate students in the first demonstration.

The values that X may take on are 0, 1, 2, and 3.

The distribution of X follows a hypergeometric distribution as we are drawing without replacement from a finite population.

We can calculate the expected number of Shotokan Karate students in the first demonstration using the formula: E(X) = (sample size / population size) * number of Shotokan Karate students = (8 / 13) * 7 ≈ 4.31. Therefore, we would expect around 4 Shotokan Karate students in the first demonstration.