A professional soccer player succeeds in scoring a goal on 84% of his penalty kicks. assume that the success of each kick is independent. (a) in a series of games, what is the probability that the first time he fails to score a goal is on his fifth penalty kick? (b) what is the probability that he scores on 5 or fewer of his next 10 penalty kicks? (c) suppose that our soccer player is out of action with an injury for several weeks. when he returns, he only scores on 5 of his next 10 penalty kicks. is this evidence that his success rate is now less than 84%? explain.

Question

Addisyn Lawson

Physics

5 November, 01:06

A professional soccer player succeeds in scoring a goal on 84% of his penalty kicks. assume that the success of each kick is independent. (a) in a series of games, what is the probability that the first time he fails to score a goal is on his fifth penalty kick? (b) what is the probability that he scores on 5 or fewer of his next 10 penalty kicks? (c) suppose that our soccer player is out of action with an injury for several weeks. when he returns, he only scores on 5 of his next 10 penalty kicks. is this evidence that his success rate is now less than 84%? explain.

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Answers (2)

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Kenyon Mcguire · Answer 1

Geometric Distributions:Deals with the number of trials required until a single success.

Geometric random variable: the number of trials (y) it takes to get a success in a geometric setting.

When do you use it? To find first success or failure

Calculator Commands

When it takes more than n trials ... 1-geometcdf (p, n)

When it take n trials ... geometpdf (p, x)

When it it takes a max of n trials ... geometcdf (p, x)

a. geometcdf (.16,5) =.0797

b. binomcdf (10,.84,5) =.013

c. From par b. if the soccer player's succes rate were still 84%, the probability that he would score 5 or few goals in 10 penalty kicks is 0.0130. This is so low thatwe should be suspicious about whether he can still hit 84% of his shots. We have convincing that his penalty kick success rate has fallen below 84%

Jacob Hayden · Answer 2

A. Using the geometric probability:.84^4 * (1-.84) = 0.07966; this means that the probability that he makes his first * the probability he makes his second * the probability he makes his third * the probability he makes his fourth * the probability he misses his fifth.

b. P (X< = 5) = binomcdf (10, 0.84, 5) = 0.0130

c. From the answer in B, if the success rate of the player still continues at 84%, the probability that he will score 5 or few goals in the 10 penalty kicks will still remain at 0.0130. This is quite low, we should examine him about whether he can still hit at 84% of his shots. So given from this data, we could say that his penalty kick success rate has fallen below the given rate of 84%.