Answer to Question #141084 in Statistics and Probability for sofia

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. What is the likelihood of 4 randomly selected games having an average point total of over 60 points?

Answer 1

Let $X=$ average point total : $X\sim N(\mu,\sigma^2/n)$

Then $Z=\dfrac{X-\mu}{\sigma/\sqrt{n}}\sim N(0,1)$

Given $\mu=42, \sigma=20, n=4$

$$P(X>60)=1-P(X\leq60)=$$

$$=1-P(Z\leq\dfrac{60-42}{20/\sqrt{4}})=1-P(Z\leq1.8)\approx$$

$$\approx1-0.96406968\approx0.03593032$$