In college basketball the home court advantage is 4 points. For example, the rec

Question

In college basketball the home court advantage is 4 points.

For example, the recent Jeff Sagarin power ratings for UNC and NC State were 82.34 and 80.50, respectively. So in a game between NC State and UNC played at NC State, the average amount by which State wins is

4 + 80.50 - 82.34 = 2.16 points

Statisticians have shown that the distribution of the final margin of victory for a home NCAA basketball team can be well-approximated using a normal model with mean = (home court advantage + home team power rating - visiting team power rating) and standard deviation 10 points.

Question 1. In a game between NC State and UNC played at NC State, what is the probability that NC State wins by at least 5 points? (If you use the Z-table, round your z-score to 2 decimal places). 

 Use 4 decimal places in your answer.

Question 2. In a game between NC State and UNC played at NC State, what is the probability that UNC wins by at least 4 points? (If you use the Z-table, round your z-score to 2 decimal places) Note: if UNC wins by at least 4 points, then NC State "wins" by -4 points or less.

Explanation / Answer

Final margin of victory for NC State (X) ~ Normal (2.16, 102)

Q1)

P(X x ) = 1 - P(X<5)

P(X 5) = 1- P(X<5)

= 1 – P((X-µ)/ < (5-2.16)/10)

=1 –P( z < 0.28) (using z table)

=1-0.6103

=0.3897

Therefore, probability that NC State wins by at least 5 points is 0.3897

Q2)

Here, we need to find the probability of NC State loses by -4 points or less.

P( X < -4) = P((X-µ)/ < (-4 - 2.16)/10)

=P(z < -0.62)

Using z table

P( z < -0.616 ) = 0 .2676

Therefore, the probability that UNC wins by at least 4 points is 0.2676.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.