Question

1. by examining past tournaments, its

possible to calculate the probability that a
school wins their first game in the national
college basketball tournament.

each schools rank going into the
tournament is a strong indicator of their
likelihood of winning their first game. this
can be expressed as ( y = - 6.83 x + 108 )
where ( x ) is their rank (out of 16) and ( y ) is
the percent chance they have of winning
their first game.

a) according to the model, a school ranked #8 has what probability of winning their first game?
round your answer to the nearest percent.
b) using this model, a school ranked #14 has what probability of winning their first game?
round your answer to the nearest percent.

Explanation:

Step1: Substitute \(x = 8\) into the equation \(y=-6.83x + 108\)

$$y=-6.83\times8+108$$
$$y=-54.64 + 108$$
$$y = 53.36$$

Step2: Substitute \(x = 14\) into the equation \(y=-6.83x + 108\)

$$y=-6.83\times14+108$$
$$y=-95.62+108$$
$$y = 12.38$$

Answer:

a) \(53\%\)
b) \(12\%\)