AP Statistics 2.10: Binomial Mean and SD
Calculate and interpret the mean and standard deviation of a binomial random variable using its number of trials and success probability.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
2.10.B—Calculate the mean and standard deviation for a binomial distribution 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.
What is the expected value for the random variable in part B (i)? Show your work.
Model Solution
E(X)=np=20(0.10)=2 songs.
Scoring component
4. Correctly calculates the expected value and shows supporting work. The parameters may also be stated here.
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