A random variable X is normally distributed with mean 70 and standard deviation 15. A. If a random sample of size 4 is selected, describe the sampling distribution of sample mean X. The distribution is ? with mean x = and standard deviation x = B. Find the probability P(X > 76.75) when n = 4. Answer: Round to 4 decimal places. C. If a random sample of size 16 is selected, describe the sampling distribution of sample mean X. The distribution is ? with mean "x = and standard deviation = D. Find the probability P(X > 76.75) when n = 16. Answer: Round to 4 decimal places. E. If a random sample of size 25 is selected, describe the sampling distribution of sample mean X. The distribution is ? with mean x = and standard deviation x= F. Find the probability P(X > 76.75) when n = 25. Answer: Round to 4 decimal places. G. Compare your answers for parts B, D and F. What is happening to the probability P(X > 76.75) as the sample size increases and why? The probability increases because the sample means become less spread out as the sample size increases. The probability decreases because the sample means become less spread out as the sample size increases. The probability increases because the sample means become more spread out as the sample size increases. The probability decreases because the sample means become more spread out as the sample size increases. Use the following built-in tool to answer the question. If at any point you wish to reset the tool to the initial state, click on the reset button below it.