Question

10 8 each]Problem 3 For a certain group of 3,000 slender men, the correlation between height and weight is8 The scatter diagram is football-shaped. The average height is 70 inches with an SD of 5 inches. The average weight is 160 pounds with an SD of 25 pounds. 13 in A) What percent of the men are taller than 6 foot, 1 inch, ie., 73 inches? 27.43% many men is this?23 men How 27 43-р О 2743(5.0): B) Given that a man weighs 210 pounds, what should you guess for his height? C) For your prediction in B), the rms size of your error, in inches, is what? 12 In D) Among men weighing 210 pounds, what percentage are taller than 6 foot? HINT: the correct procedure uses your answers to B) and C). additional pounds of E) Associated with each increase of one inch of height are weight?

Answer 1

(A)here we use standard normal variate z=(x-mean)/sd

for x=73, z=(x-mean)/sd=(73-70)/5=0.6

P(X>73)=P(Z>0.6)=1-P(Z<0.6)=1-0.7257=0.2743=27.43%

required number=n*P(X>73)=3000*0.2743=823

(B) here we use simple linear regression y(height)=a+b*x(weight)=-624+11.2*x

b=r*sd(y)/sd(x)=0.8*5/25=0.16

a=mean(y)-b*mean(x)=70-160*0.16=44.4

for x=210, y=44.4+0.16*210=78

(C) original data is needed

(D)original data is needed

(E)answer is 4

here we use simple linear regression x(weight)=a+b*y(height)

slope b=r*sd(x)/sd(y)=0.8*25/5=4

slope is the change in dependent variable with unit change in independent variable