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Assume that the heights of women are normally distributed with a mean of 62.0 inches and a standard

deviation of 2.1 inches. Find Q3, the third quartile that separates the bottom 75% from the top 25%

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Final answer:

To find the third quartile (Q3) in the normally distributed heights of women, we use the z-score for the 75th percentile and the given mean and standard deviation. The calculation results in Q3 being approximately 63.4 inches.

Step-by-step explanation:

The question asks us to find Q3, the third quartile, for the normally distributed heights of women with a mean of 62.0 inches and a standard deviation of 2.1 inches. The third quartile marks the point below which 75% of the data fall, separating the bottom 75% from the top 25%. To find the third quartile, we can use a z-score table or an inverse normal distribution calculator. The z-score corresponding to the 75th percentile in a standard normal distribution is approximately 0.674. To find Q3, we apply the formula Q3 = mean + (z-score * standard deviation), which in this case is Q3 = 62.0 + (0.674 * 2.1) inches.

By calculating this, Q3 equals approximately 62.0 + 1.4154, or 63.4154 inches. Therefore, the third quartile height is about 63.4 inches.

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