Question

A basketball player with a poor​ foul-shot record practices intensively during the​ off-season. He tells the coach that he has raised his proficiency from 55​% to 65​%. ​Dubious, the coach asks him to take 10 ​shots, and is surprised when the player hits 9 out of 10. Complete parts​ a) through​ d) below. ​a) Suppose the player really is no better than beforelong dashstill a 55​% shooter.​ What's the probability he could hit at least 9 of 10 shots​ anyway? (Hint: Use a binomial​ model.)

Answer 1

0.0232

Step-by-step explanation:

Solution:

p = 55% = 0.55

n = 10

By using binomial model of probability, we have

P = (X = k) = nCk . p°k . (1 - p)° n-k

Evaluate for (k = 9) and (k = 10)

P = (X = 9) = 10C9 . 0.55°⁹ . (1 - 0.55)° ¹⁰⁻⁹ = 0.0207

P = (X = 10) = 10C10 . 0.55°¹⁰ . (1 - 0.55)°¹⁰⁻¹⁰ = 0.0025

By adding the corresponding probabilities, we have

= 0.0207 + 0.0025

= 0.0232