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. what is an appropriate assignment of digits to the outcomes for a simulation of this random process? let 1 = the student is enrolled in the nursing program. let 2 - 5 = the student is not enrolled in the nursing program. skip the digits 6 - 9, and 0 let 0 and 1 = the student is enrolled in the nursing program. let 2 - 5 = the student is not enrolled in the nursing program. skip the digits 6, 7, 8, 9, and 0. let 1 = the student is enrolled in the nursing program. let 2 - 9 = the student is not enrolled in the nursing program. skip the digit 0 let 1 and 2 = the student is enrolled in the nursing program. let 3 - 9 = the student is not enrolled in the nursing program. skip the digit 0.

Explanation:

Step1: Analyze the proportion

Since 20% of students are in the nursing program, we need to assign 2 out of 10 non - skipped digits (digits 1 - 9 as 0 is often skipped in some digit - based simulations for simplicity) to represent students in the nursing program.

Step2: Check each option

• Option 1: Only 1 out of 5 non - skipped digits (1, 2, 3, 4, 5) represents nursing students. The proportion is \( \frac{1}{5}=20\%\) but skips too many digits (6 - 9, 0).
• Option 2: Skips 0 twice which is inconsistent.
• Option 3: Only 1 out of 9 non - skipped digits (1, 2 - 9) represents nursing students. The proportion is \( \frac{1}{9}\approx11.1\%\)
• Option 4: 2 out of 9 non - skipped digits (1, 2, 3 - 9) represent nursing students. The proportion is \( \frac{2}{9}\approx22.2\%\) which is close to 20% (and digit - based simulations can have slight approximations when using single - digit assignments. Also, 2 out of 10 digits (if we consider all 0 - 9) would be 20%, but when skipping 0, 2 out of 9 is a reasonable approximation for a digit - based simulation).

Answer:

Let 1 and 2 = the student is enrolled in the nursing program. Let 3 - 9 = the student is not enrolled in the nursing program. Skip the digit 0.