need some help with some hw

5. Let us suppose that, the weights of sumo wrestlers are Normally distributed with mean 555 lbs. and standard deviation 101 lbs. Let, X = the weight ofa randomly selected sumo wrestler. Use calculator and show all your work including proper calculator function and input for the following questions. Write correct probability notation wherever required. Round your answer to three decimal places for all numerical answers. Include units wherever required. a) (1 point) Write down the distribution of X. b) (2 points) What percentage of sumo wrestlers are expected to weigh less than 405 lbs. or more than 705 lbs.'? Also draw corresponding probability density diagram. c) (2 points) Between which two values do the middle 90% of weights lie? Also draw corresponding probability density diagram. (1) (4 points) Some people believe that the current distribution is not the correct model for sumo wrestlers' weights. Their opinion is that the Normal distribution with mean 326 lbs. and standard deviation 80 lbs. is a better model. Manny Yarbrough, a former American sumo wrestling champion, weighed roughly 700 lbs. Would Manny's weight be considered typical or unusual if i) Normal distribution with mean 555 lbs. and standard deviation 101 lbs. is considered? ii) Normal distribution with mean 326 lbs. and standard deviation 80 lbs. is considered? In both the cases, calculate the corresponding z-scores and conclude your