In the fictional country of Statanada, the weights of 18 year old boys are normally distributed with a mean of 160 pounds and a standard deviation of 20 pounds. The weights of 18 year old Statanadian girls are normally distributed with a mean of 135 pounds and a standard deviation of 17 pounds. a) Let the random variables 𝐵 and 𝐺 measure the weights of randomly selected 18 year old Statanadian boys and girls (𝐵 for boys, 𝐺 for girls). What are the mean and standard deviation of the random variables 𝐵 and 𝐺? b) Find the mean and standard deviation of the random variable 𝐵 − 𝐺. Note that 𝐸(𝐵 − 𝐺) = 𝐸(𝐵) − 𝐸(𝐺) and 𝑉𝑎𝑟(𝐵 − 𝐺) = 𝑉𝑎𝑟(𝐵) + 𝑉𝑎𝑟(𝐺). c) If a randomly selected 18 year old Statanadian boy weighs more than a randomly selected 18 year old Statanadian girl, what can you say about the value the random variable 𝐵 − 𝐺 assigns to this pair? d) The difference of two independent normally distributed random variables is another normally distributed random variable. Use this to find P(𝐵 − 𝐺 > 0). e) What is the probability that a randomly selected 18 year old Statanadian boy weighs more than a randomly selected 18 year old Statanadian girl?
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