Answer to Question #118377 in Statistics and Probability for Naa'irah

Question

Assume that the total score (from both teams) for college football games averages μ = 42 points per game, and that the distribution of total points is approximately normal with σ = 20.
a. What is the probability that a randomly selected game would have more than 60 points?
b. What proportion of college football games have a point total between 20 and 60?

Answer 1

a) Z =(x-μ)/σ=(60-42)/20=0.9

using table

P(X>60) = 1-P(z$\leq$ 0.9)=0.1841

b) x = 20 then Z =(20-42)/20= -1.1

P(-1.1<Z<0.9) =0.81594-0.13567=0.6802= 68.02%