Question

Suppose the mean and standard deviation for weights of NFL guards since 1970 is 310 lbs and 20 lbs respectively; for NFL quarterbacks since 1970 they are 220 lbs and 15 lbs, respectively. Weights within each position are bell shaped. Suppose random samples of 40 guards and 50 quarterbacks are measured and the sampling distribution is the difference in sample means, found by subtracting the quarterbacks from the guards (guards - quarterbacks).

Answer 1

answer N(90,14.5) i.e. sampling distribution is the difference in sample means will have mean =90 and stanard deviation=sqrt(14.5)=3.81

NFLgruards(x)~N(310,20*20) and

NFLquarterbacks(y)~N(220,15*15)

for x the sample size=n_x=40 and

for y the sample size=n_y=50

~N(310,20*20/40)

~N(220,15*15/50)

difrerence between mean of x and mean of y is (-)

E(-)=E()-E(?)=310-220=90

Var(-)=var()+var()=(20*20/40 + 15*15/50)=14.5

so sampling distribution is the difference in sample means will be N(90,14.5)