25. Free-throw percentage. A basketball player's free-throw percentage is 78%, meaning that for any given attempt, the probability that the shot is made is p = 0.78. Assume that each free-throw attempt is independent of the others. In one game, a player attempts 4 free throws. Let random variable X = the number of free throws the player makes. a) Find the probability mass function f(x) = P(X = x), and sketch its histogram.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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25. Free-throw percentage. A basketball player's free-throw
percentage is 78%, meaning that for any given attempt,
the probability that the shot is made is p = 0.78. Assume
that each free-throw attempt is independent of the others.
In one game, a player attempts 4 free throws. Let random
variable X = the number of free throws the player makes.
a) Find the probability mass function
f(x) = P(X = x), and sketch its histogram.
b) Find P(X = 2). What does this number represent?
c) Find P(X = 2). What does this number represent?
d) Find µ. What does this number represent?
e) Sketch a tree diagram showing all possible sequences
of successes and failures for 4 free throws.
Transcribed Image Text:25. Free-throw percentage. A basketball player's free-throw percentage is 78%, meaning that for any given attempt, the probability that the shot is made is p = 0.78. Assume that each free-throw attempt is independent of the others. In one game, a player attempts 4 free throws. Let random variable X = the number of free throws the player makes. a) Find the probability mass function f(x) = P(X = x), and sketch its histogram. b) Find P(X = 2). What does this number represent? c) Find P(X = 2). What does this number represent? d) Find µ. What does this number represent? e) Sketch a tree diagram showing all possible sequences of successes and failures for 4 free throws.
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