Answer :
Final answer:
To find the minimum weight of the middle 95% of the football players, calculate the z-score corresponding to the 97.5th percentile of the standard normal distribution and use it to find the weight using the formula x = z * standard deviation + mean. The minimum weight is 249 pounds.
Explanation:
To find the minimum weight of the middle 95% of the football players, we need to find the z-score corresponding to the 97.5th percentile of the standard normal distribution.
The z-score can be calculated using the formula: z = (x - mean) / standard deviation.
Substituting in the given values, we get: z = (x - 200) / 25. Rearranging the formula to solve for x, we get x = z * 25 + 200.
To find the z-score corresponding to the 97.5th percentile, we can use a standard normal table or a calculator. The z-score is approximately 1.96.
Substituting the z-score into the formula, we get x = 1.96 * 25 + 200 = 249 pounds.
Therefore, the minimum weight of the middle 95% of the football players is 249 pounds.
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