Question

at a large university, 20% of students are enrolled in the nursing program. the dean of students selects a random sample of 20 students and records n = the number of students enrolled in the nursing program. the dean decides to simulate this random process by using a random number table. he assigns the digits to the outcomes.
1, 2 = student enrolled in nursing program
3 - 9, 0 = student not enrolled in nursing program
here is a portion of a random number table.
table of random digits
1 31645 03495 96193 10898 88532 73869
2 67940 85019 98036 98252 43838 45644
3 21805 26727 73239 53929 42564 17080
in one trial of this simulation, 3 of the 20 randomly selected students are enrolled in the nursing program. use line 2 to complete a second trial and then use line 3 to complete a third trial. based on the results of these 3 simulations, what is the average number of students expected to be enrolled in the nursing program in random samples of size 20?

Explanation:

Step1: Count students in line 2

Line 2: 67940 85019 98036 98252 43838 45644.
We look at each digit. Digits 1 and 2 represent nursing - enrolled students.
In 67940: no 1 or 2. In 85019: digit 1. In 98036: no 1 or 2. In 98252: digit 2. In 43838: no 1 or 2. In 45644: no 1 or 2.
Count of 1s and 2s: 2.

Step2: Count students in line 3

Line 3: 21805 26727 73239 53929 42564 17080.
Digits: In 21805: digits 2 and 1. In 26727: digits 2 and 2. In 73239: digit 2. In 53929: digit 2. In 42564: digit 2. In 17080: digit 1.
Count of 1s and 2s: 7.

Step3: Calculate the average

We have three trials: 3 (given), 2 (from line 2), 7 (from line 3).
The formula for the average $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 3$, $x_1=3$, $x_2 = 2$, $x_3=7$.
$\bar{x}=\frac{3 + 2+7}{3}=\frac{12}{3}$

Answer:

4