In a basketball match, a shooting guard can either throw the ball in the basket and score points for his team or miss it and not score. Each successful basket is worth one point. Which distribution best describes this scenario?

A. Binomial distribution
B. Poisson distribution
C. Normal distribution
D. Exponential distribution

Question

28-05-2024
Social Studies

High School

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In a basketball match, a shooting guard can either throw the ball in the basket and score points for his team or miss it and not score. Each successful basket is worth one point. Which distribution best describes this scenario?

A. Binomial distribution
B. Poisson distribution
C. Normal distribution
D. Exponential distribution

Answer :

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gayathrikse121 gayathrikse121 · Answer 1 · 2023-10-04T00:03:37-04:00

Final answer:

In the context of a basketball match with shots being either successful or missed, the correct distribution is the binomial distribution. Shots are considered independent trials with two outcomes, and calculation of mean and standard deviation is possible with known probabilities of success and failure. The running example describes an exponential distribution.

Explanation:

The scenario described in the basketball match question pertains to a binomial distribution. A binomial distribution involves a fixed number of independent trials, each with only two possible outcomes, termed success and failure. In this case, each shot by the shooting guard is an independent trial with a success being scoring a point and a failure being a missed shot. The number of successes can be calculated using the formula μ = np, where μ is the mean, n is the number of trials, and p is the probability of success. The standard deviation is given by the formula σ = √npq, with q representing the probability of failure.

When looking at the distribution described by the example of people running different distances, the appropriate distribution is the exponential distribution. This distribution reflects the principle that as the distance increases, the likelihood of individuals being able to run that far decreases at an exponential rate.