To find the percentile of a height of 79 inches in a bell-shaped distribution with a mean of 72.5 inches and a standard deviation of 3.25 inches, you can use the standard normal distribution (Z-score).
First, calculate the Z-score for a height of 79 inches using the formula:
Z = (X - μ) / σ
Where:
X is the value you want to find the percentile for (79 inches in this case).
μ (mu) is the mean of the distribution (72.5 inches).
σ (sigma) is the standard deviation (3.25 inches).
Z = (79 - 72.5) / 3.25
Z = 6.5 / 3.25
Z = 2
Now that you have the Z-score of 2, you can find the percentile using a standard normal distribution table or calculator. A Z-score of 2 corresponds to the 97.72nd percentile.
So, a height of 79 inches is at approximately the 97.72nd percentile in this distribution. This means that 79 inches is taller than approximately 97.72% of the basketball players in this dataset.