Suppose, at a local movie theater, the amount of money that a man spends at the concession has an average of 16 dollars and a standard deviation of 5.0 dollars. As well, the amount of money twat a woman spends at the concession has an average of 12 dollars and a standard deviation of 3.4 dollars. (a) What is the expected difference in the amount spent by a man and a woman at the concession? Answer: dollars (b) What is the standard deviation for this difference? (Round your answers to four decimal places, if needed.) Answer: dollars (c) What is the expected tota amount spent by a man and a woman at the concession? Answer: dollars (d) What is the standard deviation for this total amount? (Round your answers to four decimal places, if needed.) Answer: dollars Claire and George are tasked with decorating Easter eggs The amount of eggs that Claire can decorate in an hour is a random variable with M : 17 and a : 3' The amount of eggs that George can decorate in an hour is a random variable with p = 13 and (r = 5. Assume the amount of eggs Claire and George decorate are independent of each other. (Round your answers to four cecimal places, if needed.) (a) What is the mean for the total number of eggs they decorate in an hour? Answer: (b) What is the standard deviation for the total number of eggs they decorate in an hour? Answer: (c) Claire decides to decorate Easter eggs for one hour today and for another hour tomorrow. What is the expected value of the total number of eggs she will decorate in total? Answer: (d) Claire decides to decorate Easter eggs for one hour today and for another hour tomorrow. What is the standard deviation of the total number of eggs she will decorate in total? Answer: Check A manufacturer produces items with a rectangular base. Let random variables denote the respective length (X) and width ()) of the rectangle (in cm). Suppose X and Y are independent with the following parameter values. E(X) = 4, Var(X) = 0.14, E()) = 10, Var()) = 0.39 The perimeter is then defined as 2X + 2Y. (Round your answers to 4 decimal places, if needed.) (a) What is the mean of the perimeter of the rectangle? (b) What is the standard deviation of the perimeter of the rectangle?Say you have a biased coin and you associate obtaining a head with the value 0 whereas obtaining a tail has a value of 2, Let X be the sum of the values obtained from tossing the coin three times, (Round your answers to 4 decimal places, if needed.) (a) If the probability of getting heads in a single toss is 0.38, then what is the probability distribution ofX ? (b) What is P(X