Data from a National Health Survey show that menâ’s average weight is normally

3. Data from a National Health Survey show that men’s average weight is normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.a. If a man is chosen at random, what is the probability that his weight is greater than 180 pounds?b. If 100 men are randomly selected, what is the probability that their mean weight is greater than 180 pounds?c. What is the probability that mean weight of the 100 men is less than 160 pounds?4. According to the College Board’s report, the average tuition and fees at four year private colleges and universities in the United States was $18,273 for the academic year 2002 – 2003 and the standard deviation was $2100. For a random sample of 100 four year private U.S. colleges:a. What is the mean of the sampling distribution?b. What is the standard deviation of the sampling distribution?c. What is the probability that the mean tuition and fees of the sample is greater than $20,000?d. What is the probability that the mean tuition and fees of the sample is less than $16,000?e. What is the probability that the mean tuition and fees of the sample is within $550 of the population mean?