Question

statistics chapter 4 practice test – fall semester 2025 – ahs – room 404 – mr scheel

1. for each scenario listed, determine whether it would best be represented by a continuous or discrete random variable:

a. the amount of water in amphis pool
b. the number of students attending a basketball game
c. the money it costs for a graduation cap and gown
d. the height of mount lemmon
e. the time it takes to get through the line at the dmv
f. the number of ahs seniors that will graduate
g. total points scored by a football team

Explanation:

Step1: Recall definitions

A discrete random variable has a countable number of possible values. A continuous random variable can take on any value in an interval.

Step2: Analyze each scenario

• A. The amount of water in Amphi’s pool:

Water amount can take any value within a range (e.g., 100.5 gallons, 100.55 gallons). So it is a continuous random variable.

• B. The number of students attending a basketball game:

Number of students is a countable quantity (e.g., 100 students, 101 students). So it is a discrete random variable.

• C. The money it costs for a graduation cap and gown:

Money can be measured with arbitrary precision (e.g., \(\$100.50\), \(\$100.51\)). So it is a continuous random variable.

• D. The height of Mount Lemmon:

Height can take any value within a range (e.g., \(9157.5\) feet, \(9157.55\) feet). So it is a continuous random variable.

• E. The time it takes to get through the line at the DMV:

Time can take any value within a range (e.g., \(10.5\) minutes, \(10.55\) minutes). So it is a continuous random variable.

• F. The number of AHS seniors that will graduate:

Number of seniors is a countable quantity (e.g., 200 seniors, 201 seniors). So it is a discrete random variable.

• G. Total points scored by a football team:

Points are countable (e.g., 10 points, 11 points). So it is a discrete random variable.

Answer:

A. Continuous, B. Discrete, C. Continuous, D. Continuous, E. Continuous, F. Discrete, G. Discrete