Question

Let $X=$ height (inches) and $Y=$ weight (lbs) for an American male. Suppose $X$ and $Y$ have a bivariate normal distribution, the mean and sd of heights are 70 in and 3 in. the mean and sd of weights are 170 Ibs and 20 lbs, and the correlation coefficient is $\rho=.9$ (a) Determine the distribution of $Y$ given $X=68,$ i.e., the weight distribution for $5^{\prime} 8^{\prime \prime}$ American males. (b) Determine the distribution of $Y$ given $X=70,$ i.e., the weight distribution for $5^{\prime} 10^{\prime \prime}$ American males. In what ways is this distribution similar to that of part (a), and how are (c) Calculate $P(Y<180 | X=72),$ the probability that a 6 -ft-tall American male weighs less than 180 $\mathrm{lb}$ .

          Let $X=$ height (inches) and $Y=$ weight (lbs) for an American male. Suppose $X$ and $Y$ have a
bivariate normal distribution, the mean and sd of heights are 70 in and 3 in. the mean and sd of weights are 170 Ibs and 20 lbs, and the correlation coefficient is $\rho=.9$
 
(a) Determine the distribution of $Y$ given $X=68,$ i.e., the weight distribution for $5^{\prime} 8^{\prime \prime}$ American males.
(b) Determine the distribution of $Y$ given $X=70,$ i.e., the weight distribution for $5^{\prime} 10^{\prime \prime}$ American males. In what ways is this distribution similar to that of part (a), and how are
(c) Calculate $P(Y<180 | X=72),$ the probability that a 6 -ft-tall American male weighs less than 180 $\mathrm{lb}$ .

Added by Shane C.

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