Respuesta :
Since the mean height of all children this age is 38 inches, the z-score is 1.282, and the child's height is 40 inches, the standard deviation of all children's heights will be 1561.
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
Here,
The z-score which separates the top 10% of a normally distributed
population is 1.282.
Since z = (x-u)/sigma
1.282 = (40-38)/sigma
sigma = 2/1.282
sigma = 1/0.641 = 1561
The standard deviation of the heights of all children of this age will be 1561 as mean is 38 inch and z-score is 1.282 as well as the height of child is 40 inch.
To know more about standard deviation,
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