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.

b. What proportion of college football games have a point total between 20 and 60?

Answer 1

Let $X$ has normal distribution $X$~$N(42,20^2)$, then $Z=\frac{X-42}{20}$~$N(0,1)$,

$P(20<X<60)=\\ P(\frac{20-42}{20}<\frac{X-42}{20}<\frac{60-42}{20})=\\ P(-1.1<Z<0.9)=\\ P(Z<0.9)-P(Z\leq -1.1)\approx\\ 0.8159-0.1357=0.6802.$

Approximately $100*0.6802$%$=68.02$% of games have a point total between 20 and 60.

Answer: 68.02%.