Practise calculating the mean and standard deviation of a binomial count from its number of independent trials and constant probability of success.
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.