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If the average (mean) mid-twenties male weighs 169 pounds and a weight of 151 is in the 31st percentile, what is the standard deviation of the weights in this age group? Round your answer to two decimal places.

Answer :

Final answer:

To find the standard deviation of the weights in this age group, use the formula σ = (x - μ) / z, where x is the weight, μ is the mean, and z is the z-score. The standard deviation is approximately 45.23 pounds.

Explanation:

To find the standard deviation of the weights in this age group, we need to use the information provided. We know that the average weight is 169 pounds and a weight of 151 is in the 31st percentile.

First, we need to find the z-score for a weight of 151 using the formula z = (x - μ) / σ, where x is the weight, μ is the mean, and σ is the standard deviation. Rearranging the formula, we have σ = (x - μ) / z.

Using the percentile-to-z-score conversion table, we can find that the z-score corresponding to the 31st percentile is approximately -0.398. Plugging in the values, we have σ = (151 - 169) / -0.398 ≈ 45.23 pounds. Therefore, the standard deviation of the weights in this age group is approximately 45.23 pounds.

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