Final answer:
The mean of Corey Pebbleman's scores in basketball games is calculated as the number of shots multiplied by the probability of scoring, which is 49.04 points for the given player.
Step-by-step explanation:
The average number of points scored by Corey Pebbleman in basketball games is the mean of his scores, while the standard deviation is a measure of the variation or dispersion of his scores from the mean.
Calculating the Mean and Standard Deviation
To calculate the mean (μ) of X, the number of successful shots, you would use the formula μ = n * p, where n is the number of shots and p is the probability of making a shot. Using the information given for a player with a 61.3 percent success rate on 80 shots:
Mean (μ) = 80 * 0.613 = 49.04
To calculate the standard deviation (σ), you would use the formula σ = √(n * p * q), where q is the probability of missing a shot (1 - p).
Standard deviation (σ) = √(80 * 0.613 * (1 - 0.613)) = √(80 * 0.613 * 0.387) ≈ 4.36
The standard deviation, which measures the score variability, can be found using the square root of the product of the number of shots, the probability of scoring, and the probability of not scoring, resulting in approximately 4.36 for the given player.