3. Let us suppose that the weighits and standard deviation 101 lbs. Let, X = the weight of a 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 . X N ( u 555 lbs, . 101 lbs ) b) (3 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. P ( 405 < x < 705 ) = P ( x < 705 ) P ( x < 405 ) = P ( x 4/0 ) < ( 705 555 ) //01 ) P ( x 4/ r ) < ( 405 55 ) = P ( 2 < 1.49 ) P ( 2 < 149 ) = 0.4319 0.0681 = 0.8658 = 86.4% c) (3 points) Between which two values do the middle 90% of weights lie? Also draw corresponding probability density diagram. d) (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 umusual 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 answer..

1. 3. Let us suppose that the weighits and standard deviation 101 lbs. Let, X = the weight of a
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 . X N ( u 555 lbs, . 101 lbs
) b) (3 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. P ( 405 < x < 705 ) =
P ( x < 705 ) P ( x < 405 ) = P ( x 4/0 ) < ( 705 555 ) //01 ) P ( x 4/ r ) < ( 405 55 ) = P ( 2 < 1.49 )
P ( 2 < 149 ) = 0.4319 0.0681 = 0.8658 = 86.4% c) (3 points) Between which two values do the
middle 90% of weights lie? Also draw corresponding probability density diagram. d) (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 umusual 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 answer.