A random variable X is normally distribured with mean 40 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 > 45.1) 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 disriburion is with mean #x= and scandard deviation ~ x D. Find the probability P(X > 45.1) 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 > 45.1) when n - 25. Answer. Round to 4 decimal places. G. Compare your answers for parts B. D and [. What is happening on the probability P(X > 45.1) as the sample size increases and why? O The probability decreases because the sample means become less spread out as the sample size increases. The probability increases because the sample means become less spread out as the sample size increases. 3 The probability decreases because the sample means become more spread out as the sample size increases The probability increases because the sample means become more spread out as the sample size increases. Use the following built in pool no answer the question. If at any point you wish to reset the cool to the initial scare, click on the "reser" bucron below ic. Distribution Statistics 1= 00=1 |Normal * 15 1 FR37