Stats questions PLease help?

Assume the heights if high school basketball players are normally distributed, For boys the mean is 74 inches with a std. dev. of 4.5 in., while for the girls the mean in 70 in. w/ a std. dev. of 3 in. At a mixed 2 - on - 2 tournament teams are formed by randomly pairing boys with girls as teammates.





On what fraction of teams would you expect the girl to be taller than the boy?








Which of the following has a Binomial model?





A. The # of people we survey untill we find someone who has taken Stats.


B. the # of people we survey untill we find 2 people who have taken Stats.


C. The # of people in a class who have taken Stats.


D. The # of aces in a five card poker hand.


E. The # of sodas students drink per day.

Stats questions PLease help?
Always set up problems like this by identifying your R.V.


Let X = height of guy and Y = height of girl such that:


X ~ N(74, 4.5)


Y ~ N(70, 3)


You need to find P(X %26lt; Y) = P(X - Y %26lt; 0)


So you also need to find the difference of Expectation and Variance.


E[X-Y] = E[X] - E[Y] = 74 - 70 = 4


Var[X - Y] = Var[X] + Var[Y] = 4.5^2 + 3^2 = 11.25


so the Standard Deviation is 3.354...


No that's not a typo, it's PLUS. The formula is actually Var[X - Y] = Var[X] + Var[Y] +2abCov(X,Y) but since we can assume that X and Y is independent (DUH!) then Cov(X,Y) = 0.





Using the formula for Normal Distribution:


P((X-Y-E[X-Y] ) / sqrt(Var[X - Y]) %26lt; 0 -E[X-Y] / sqrt(Var[X - Y]) )


= Phi(Z %26lt; -1.19)


= 1 - Phi(1.19)


= 1 - .8830 using the Normal Distribution table


= .117





So what does this mean?


.117 is the probability that in a team of a boy and a girl, there is a 11.7% that the girl will be taller than the boy. Put that in fraction form and you're done.








Which of the following has a Binomial model?


Answer:


C. The # of people in a class who have taken Stats.


Because a binomial model requires only 2 possibility/outcome, i.e. success or failure. Here, it's people who have taken Stats and those who haven't.





A. is geometric


B. is Negative Binomial


D. is Hypergeometric


E. is just silly...