Answer :
Final answer:
In a normal distribution of college women's heights with a mean of 65 inches and standard deviation of 2.5 inches, a height of 97.5 inches is highly unusual and lies many standard deviations above the mean.
Explanation:
This question pertains to the standard deviation and the properties of a normal distribution curve in mathematics. The mean height of college women is given as 65 inches with a standard deviation of 2.5 inches. This means that most college women's heights will fall within the range of 62.5 to 67.5 inches if we consider one standard deviation from the mean.
However, the question asks for the height that falls at 97.5 inches, which is many standard deviations above the mean. In a normal distribution, approximately 99.7% of all values fall within three standard deviations from the mean. Going beyond that is highly unusual in a normal distribution. Hence, a woman's height being 97.5 inches would be extraordinarily rare and well beyond what is expected in a typical normal distribution. Note that this is based on the assumption of the heights being normally distributed, and in reality, such extreme values could exist.
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