AP Statistics 2.10: Binomial Random Variables
Decide whether a count is binomial by checking a fixed number of independent trials, two outcomes, and a constant success probability.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
2.10.A—Justify why a random variable is or is not a binomial random variable question 1
Ms. Fey is a manager at a restaurant. To improve the dining experience for her customers, she
uses a digital music service to create a playlist of songs that will be played in the restaurant.
The playlist contains 1,000 songs and consists of four different types of music in the following
quantities: 200 country songs, 400 pop songs, 100 rock songs, and 300 jazz songs. The digital
music service will select songs at random from the playlist to be played in the restaurant. Any
song can be replayed at any time.
In every one-hour period, 20 songs will be played at random and any song can be replayed at
any time. Ms. Fey is interested in how many rock songs will be played in a typical one-hour
period.
Define the random variable of interest to Ms. Fey, and state how the random variable is
distributed.
Model Solution
Let X be the number of rock songs among the 20 songs played in one hour. Since songs are selected independently with replacement and p=100/1000=0.10, X has a binomial distribution with n=20 and p=0.10.
Scoring components
1. Defines the random variable as the number of rock songs in one hour.
2. Identifies a binomial distribution.
3. States n=20 and p=0.10.
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