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 ๐ต and ๐บ measure the weights of randomly selected 18 year old Statanadian boys and girls (๐ต for boys, ๐บ for girls). What are the mean and standard deviation of the random variables ๐ต and ๐บ? b) Find the mean and standard deviation of the random variable ๐ต โ ๐บ. Note that ๐ธ(๐ต โ ๐บ) = ๐ธ(๐ต) โ ๐ธ(๐บ) and ๐๐๐(๐ต โ ๐บ) = ๐๐๐(๐ต) + ๐๐๐(๐บ). 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 ๐ต โ ๐บ 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(๐ต โ ๐บ > 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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