3] {40 point.) Sam la a. UT super-fan that has twenty UT t-shlrts. There are 12 orange. 5 white and 3 smokey gray tshirts in Sam's closet. Every time there is s UT home game In any sport, Sam randomly grabs a t-shirt from the closet to wear that day. Sam is very superstitious and hand washes and blow dries each shirt the clay it is worn so it Is available for the next day. Suppose Sam attends 100 home games in a year. A] What is the probability that Sam wears an orange shirt to any random home game? Consider the set of all possible samples 100 home games and the proportion of orange shirts that Sam wears to them. What is the mean and stmdard deviation for the population of all such possible sample proportions? a] i\"? c; 0'; D) Explain why the proportion of orange shirts that Sam wears to the 100 home games can be approximted by a normal distribution. E) What is the probability that Sam wears an orange shirt to more than 65% of the 100 or home games? Show the work. . ., ' ' 10(13 > 0.65) =