Sofia's audio player has 15,000 songs. The play time for the songs is skewed to the right, with a mean of 255 seconds and a stan
dard deviation of 30 seconds. Part A: Can you accurately calculate the probability that the mean play time is more than 260 seconds for an SRS of 15 songs? Explain. (4 points) Part B: If you take a random sample of 40 songs instead of 15, explain how the Central Limit Theorem allows you to find the probability that the mean play time is more than 260 seconds. Calculate this probability and show your work. (6 points)
You can not accurately calculate this because the SRS is not over 30. The CLT states that if the sample size is big enough, it will have a normal distribution. 15 is not big enough.
Part B
You can calculate this because the sample size is over 30; in this case, it is 40. So first, we have to find the standard deviation of the sampling distribution of the means. Which is done by taking the standard deviation and dividing it by the square root of the sample size, which comes out to be 4.74341649. Next, we throw it into the calculator in Normal CDF (260,9999,255,4.74341649). The final answer comes out to be 14.59%.
