From data adapted from the National Center for Health Statistics, the height in inches and age in years for boys between 4 and 16 years of age are related according to . To account for normal variability among boys, normal height for a given age is of the height obtained from the equation. Find the inequality which represents the normal height range for a boy who is 11.25 years old. Round your answer to two decimal places.

Question

From data adapted from the National Center for Health Statistics, the height  in inches and age  in years for boys between 4 and 16 years of age are related according to  . To account for normal variability among boys, normal height for a given age is  of the height obtained from the equation. Find the inequality which represents the normal height range for a boy who is 11.25 years old. Round your answer to two decimal places. ​

Quizplus · Accepted Answer

Substitute 11.25 for age in the given equation to find the expected height for a boy who is 11.25 years old.
 
height = 30.14 + 1.844(age) - 0.02(age)^2
height = 30.14 + 1.844(11.25) - 0.02(11.25)^2
height = 58.49 inches
 
To find the normal height range, we need to find the range of heights that are within one standard deviation of the expected height. To do this, we need to find the standard deviation of heights for 11.25-year-old boys. We are given that the standard deviation of heights for boys of a given age is 5% of the expected height, so:
 
standard deviation = 0.05(expected height)
standard deviation = 0.05(58.49)
standard deviation = 2.92 inches
 
Thus, the normal height range for a boy who is 11.25 years old is:
 
normal range = (expected height - standard deviation, expected height + standard deviation)
normal range = (58.49 - 2.92, 58.49 + 2.92)
normal range = (55.57, 61.41)
 
Therefore, the inequality which represents the normal height range for a boy who is 11.25 years old is: 
55.57 ≤ height ≤ 61.41
Which is equivalent to: 
 
11eb0d3b_975d_2ee2_9790_eb54bd29fe35_TB1243_11

From Data Adapted from the National Center for Health Statistics