Final answer:
The expected number of music students on the honor roll is calculated using the product of probabilities of being a music student, being on the honor roll, and the total number of students, resulting in 16 students. The guitar has the lowest cost compared to its mean, while the piano has the highest cost compared to its mean but is less of an outlier due to the higher standard deviation.
Step-by-step explanation:
The subject of this question is Mathematics, specifically related to statistics and probability. When addressing the question about the expected number of music students who are also on the honor roll, given that being a music student and being on the honor roll are independent events, we use the concept of expected value.
To calculate this, we multiply the probability of being a music student (50/300) by the probability of being on the honor roll (97/300) and then multiply the result by the total number of students. The expected number is then (50/300) * (97/300) * 300 = 16.17, which can be rounded to 16 students.
For the question about purchasing musical instruments, considering the mean cost and standard deviation, the cost that is the lowest when compared to other instruments of the same type is the guitar, because it is priced at $550 while the mean cost is $500 with a standard deviation of $200. The cost that is the highest is the piano, as it costs $3,000, whereas the mean cost for a piano is $4,000 but with a high standard deviation of $2,500, making the actual purchase price less of an outlier than the guitar's.