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Answer :
Final answer:
Using the z-score formula, the weight of 99 pounds in a population where the mean weight is 162 pounds and the standard deviation is 24.3 pounds gives a z-score of -2.59. This value is significantly below the mean, so the weight of 99 pounds is considered below average.
Explanation:
The z-score can be obtained through the formula z = (X - μ) / σ where X is the raw score, μ is the mean, and σ is the standard deviation. In this case, X = 99 pounds, μ = 162 pounds, and σ = 24.3 pounds. Plugging these values into the formula will give us our z-score.
So, z = (99 - 162) / 24.3 = -2.59 approximately.
Typically, if a z-score is less than -3 or greater than 3, it is considered highly unusual. However, in this instance, a z-score of -2.59 suggests a weight that is significantly below average. Therefore, the 99 pounds weight is considered below average for this given population.
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