Practise interpreting binomial probabilities, expected counts, and standard deviations in context, then use unusual outcomes to evaluate a chance-process claim.
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.
Recall that in every one-hour period, 20 songs will be played at random and any song can be replayed at any time.
Suppose 4 rock songs are played during a particular one-hour period. Does this provide strong evidence that the song selection process was not truly random? Justify your answer without performing an inference procedure.
Model Solution
No. The probability of four or more rock songs is 0.133, which is high enough to be reasonably attributed to chance alone and is not small enough to provide strong evidence that the selection process was not truly random.
Scoring components
3. Indicates there is not a strong reason to believe the process was not random.
4. Correctly links the probability to that decision.