A survey shows that 60% of people who listen to a song on the internet will buy the song. A sample of 30 people who listened to a song is taken. What will be the mean and standard deviation of the number who will buy the song?

To find the mean and standard deviation of the number of people who will buy the song, we need to use the concept of binomial distribution since it involves a percentage/fraction. The binomial distribution is applied when there are only two possible outcomes: success or failure.

In this case, success is defined as someone buying the song (60% probability), and failure is defined as someone not buying the song (40% probability).

Mean (μ) of a binomial distribution is given by:
μ = n * p
where n is the sample size and p is the probability of success.

Standard deviation (σ) of a binomial distribution is given by:
σ = √(n * p * (1 - p))

Given that the sample size (n) is 30 and the probability (p) is 0.6, we can calculate the mean and standard deviation.

Mean (μ) = 30 * 0.6 = 18

Standard deviation (σ) = √(30 * 0.6 * 0.4) = √(7.2) ≈ 2.683

Therefore, the mean number of people who will buy the song is 18, and the standard deviation is approximately 2.683.