Final answer:
Tom Brady's height of 6 feet 4 inches places him just below the 98th percentile among NFL football players based on the calculation of the z-score of approximately 1.9565.
Step-by-step explanation:
To determine what percentile Tom Brady's height places him in among NFL football players, we need to calculate his z-score based on the provided information that the heights are approximately normally distributed with a mean of 71.5 inches and a standard deviation of 2.3 inches. Tom Brady's height is 6 feet 4 inches, which equals 76 inches (because 1 foot equals 12 inches, so 6 feet equals 72 inches plus the additional 4 inches).
The z-score formula is:
z = (X - μ) / σ
where X is Tom Brady's height (76 inches), μ (mu) is the mean height (71.5 inches), and σ (sigma) is the standard deviation (2.3 inches).
Substituting these values into the formula, we get:
z = (76 - 71.5) / 2.3 = 4.5 / 2.3 ≈ 1.9565
Now we consult a standard normal distribution table (or use a calculator with statistical functions) to find the percentile corresponding to a z-score of approximately 1.9565. This z-score corresponds to a percentile just below the 98th percentile.
Therefore, Tom Brady's height places him just below the 98th percentile among NFL football players, which means option b. 98th would be the correct answer.