The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aaliyah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aaliyah's height, and how does her height compare to Jayne's height?

Question

Mathematics

Jasmine Gregory

11 April, 03:48

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aaliyah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aaliyah's height, and how does her height compare to Jayne's height?

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Answers (1)

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Allie Rowland · Answer 1

Aaliyah's height is the 84th percentile and the relationship that there exists between Aaliyah's height and between Jayne's height is that Aaliyah's height is less than Jayne's height.

Step-by-step explanation:

Below we can observe the empirical rule with a mean of 46.0 inches and a standard deviation of 2.7 inches. We have that 48.7 inches represents one standard deviation above the mean, so, we can consider that Aaliyah's height is the 84th percentile. On the other side, Jayne's height is the 93rd percentile of the height distribution. Therefore, the relationship that there exists between Aaliyah's height and between Jayne's height is that Aaliyah's height is less than Jayne's height.