Question

a professional basketball player typically attempts 8 free throws per game. let x represent the number of free throws made out of 8. the distribution for x is shown in the table. what is the median of the distribution? 4 4.5 4.8 5

Explanation:

Step1: Calculate cumulative probabilities

Cumulative probability for \(0\): \(P(X = 0)=0.002\)
Cumulative probability for \(1\): \(P(X\leq1)=0.002 + 0.008=0.01\)
Cumulative probability for \(2\): \(P(X\leq2)=0.01+0.04 = 0.05\)
Cumulative probability for \(3\): \(P(X\leq3)=0.05 + 0.12=0.17\)
Cumulative probability for \(4\): \(P(X\leq4)=0.17+0.23 = 0.4\)
Cumulative probability for \(5\): \(P(X\leq5)=0.4+0.28 = 0.68\)

Step2: Determine the median

The median \(M\) is the value such that \(P(X\leq M)\geq0.5\) and \(P(X\geq M)\geq0.5\).
Since \(P(X\leq4) = 0.4<0.5\) and \(P(X\leq5)=0.68\geq0.5\)

Answer:

\(5\)