Question

Part A: Can you accurately calculate the probability that the mean playtime is more than 142 seconds for an SRS of 10 videos? Explain.

a. Yes, I can accurately calculate it because the sample size is large enough.
b. No, I cannot accurately calculate it because the sample size is too small.
c. Yes, I can accurately calculate it using the Central Limit Theorem.
d. No, I cannot accurately calculate it using the Central Limit Theorem.

Part B: If you take a random sample of 50 videos instead of 10, explain how the Central Limit Theorem allows you to find the probability that the mean playtime is more than 142 seconds. Calculate this probability and show your work.

a. The Central Limit Theorem doesn't apply to this situation.
b. The Central Limit Theorem allows you to approximate the distribution of sample means. You can calculate the probability using the z-table.
c. The Central Limit Theorem allows you to calculate the exact probability.
d. The Central Limit Theorem only works for sample sizes below 30.

Answer 1

c. Yes, I can accurately calculate it using the Central Limit Theorem. b. The Central Limit Theorem allows you to approximate the distribution of sample means.

Step-by-step explanation:

Part A: The correct answer is c. Yes, I can accurately calculate it using the Central Limit Theorem. The Central Limit Theorem states that for large sample sizes, the sampling distribution of the mean will be approximately normally distributed, regardless of the shape of the population distribution. In this case, since the sample size is 10, it is considered to be large enough for the Central Limit Theorem to apply. Therefore, we can use the properties of the normal distribution to calculate the probability that the mean playtime is more than 142 seconds.

Part B: The correct answer is b. The Central Limit Theorem allows you to approximate the distribution of sample means, even when the population distribution is not normal. By taking a larger sample size of 50 videos instead of 10, the Central Limit Theorem still applies and allows us to use the properties of the normal distribution to calculate the probability. To find the probability that the mean playtime is more than 142 seconds, we can calculate the z-score and use the z-table.