Final answer:
The student's question pertains to mathematical concepts of probability distribution, mean, and standard deviation in the context of a basketball player's shooting percentage. Players improve shooting accuracy through repetitive practice, drills, coaching, and technological analysis.
Step-by-step explanation:
The question refers to the calculation of probabilities and statistics related to basketball free throw shooting, which is a mathematical concept. Specifically, the student is asking how to determine a probability distribution for the number of successful field goals out of a sample and how to calculate the mean and standard deviation for a given player's shooting percentage.
For the player with a 61.3 percent field goal completion rate, if we look at a sample size of 80 shots:
- a. The probability distribution for X (the number of shots scored) would follow a binomial distribution, with p (probability of success on each trial) being 0.613.
- b. (i) The mean (μ) of X can be calculated using the formula μ = n * p, where n is the number of trials and p is the probability of success on each trial.
- b. (ii) The standard deviation (σ) of X can be determined using the square root of the formula σ^2 = n * p * (1 - p).
In context to Brian Robertas' situation, a similar application of probability and statistics could determine the impact of his missed shot on his overall free throw percentage.
Improving Shooting Accuracy
To improve shooting accuracy, professional basketball players often engage in rigorous training, including practicing their shots repeatedly, using shooting drills, receiving coaching feedback, and using technology to analyze and correct their shooting form. Understanding the science behind the shot and muscle memory is key to increasing accuracy.