Using the health records of ever student at a high school, the school nurse created a scatterplot relating y = height (in centimeters) to x = age (in years).

naivlingr 2021-01-10 Answered

Using the health records of ever student at a high school, the school nurse created a scatterplot relating y = height (in centimeters) to x = age (in years).
After verifying that the conditions for the regression model were met, the nurse calculated the equation of the population regression line to be μ0=105+4.2x with σ=7cm.
About what percent of 15-year-old students at this school are taller than 180 cm?

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Expert Answer

Delorenzoz
Answered 2021-01-11 Author has 91 answers

Step 1
Given:
μy=105+4.2x (Equation population regression line)
σ=7
The average height of 15-year-old students at this high school according to the population regression line can be found by replacing x in the regression line equation by 15 and evaluating.
μy=105+4.2(15)=105+63=168
Thus the mean is 168 and the standard deviation is 7.
Since the conditions are met, the response y varies according to a Normal distribution.
The z-score is the value decreased by the mean, divided by the standard deviation.
z=xμσ=18016871.71
Determine the corresponding probability using the normal probability table in the appendix. P(Z<1.71) is given in the row starting with 1.7 and in the column starting with .01 of the standard normal probability table in the appendix.
P(X>180)=P(Z>1.71)
=1P(Z<1.71)
=10.9564
=0.0436
=4.36%
Thus about 4.36% of the 15-year-old students at this school are expected to be taller than 180 cm.
Result: 4.36%

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