Question

28. Suppose we have a random sample of size 49 coming from a Gamma distribution with parameters \( \alpha = 5 \) and \( \beta = 2 \). Let \( \overline{X} \) denote the sample mean. Use the central limit theorem to approximate the following probability (the final answer must be in terms of the cdf of the standard normal distribution) \( P(|\overline{X} - 8| > 3) \).

          28. Suppose we have a random sample of size 49 coming from a Gamma distribution with parameters \( \alpha = 5 \) and \( \beta = 2 \). Let \( \overline{X} \) denote the sample mean. Use the central limit theorem to approximate the following probability (the final answer must be in terms of the cdf of the standard normal distribution)
\( P(|\overline{X} - 8| > 3) \).

28. Suppose we have a random sample of size 49 coming from a Gamma distribution with parameters α = 5 and β = 2. Let X denote the sample mean. Use the central limit theorem to approximate the following probability (the final answer must be in terms of the cdf of the standard normal distribution)
P(|X - 8| > 3).

Added by Samuel N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Danielle Fairburn

11/26/2023

Step 1

So, the mean of the Gamma distribution in this problem is 5/2 = 2.5. Show more…

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28. Suppose we have a random sample of size 49 coming from a Gamma distribution with parameters α = 5 and β = 2. Let X denote the sample mean. Use the central limit theorem to approximate the following probability (the final answer must be in terms of the cdf of the standard normal distribution) P(X-8 > 3).