Question

Use the following scenario and data for questions 6 to 13: About 23.3% of the freshmen enrolled in a state university are first generation college students, i.e., equation. An officer at student affairs randomly selected a sample of equation freshmen for a panel discussion. Use equation to denote the number of first generation college students in this sample. Keep at least 4 decimal digits if the result has more decimal digits. The expected value equation of equation is 1.5242 2.3232 3.0290 9.9710 none of the above

Answer 1

E(X)= 3.029

Explanation:

Hello!

The variable of interest is

X: The number of first-generation college students in a sample of 13 college students.

The population proportion of the freshmen that are first-generation college student is 23.3%

This variable is discrete.

Considering the binomial criteria:

1. The number of observations of the trial is fixed, each repetition has two possible outcomes, "success": the student is first-generation college student, or "failure": the student isn't a first-generation college student.

2. Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial

3. The probability of success in the same from one trial to another

So X≈ Bi (n;ρ)

n= 13 p=0.233

For the binomial distribution the expected value is:

E(X)= n*p= 13*0.233= 3.029.

I hope it helps!