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

Wierzycaz 2020-11-10 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=7 cm. About what percent of 15-year-old students at this school are taller than 180 cm?
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Expert Answer

Aniqa O'Neill
Answered 2020-11-11 Author has 100 answers

Given: (Equation population regression line): μy=105 + 4.2x
σ=7 The average height of 15-year-old students at this high scool 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 is7. 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= x  μσ= 180  1687  1.71 Determine the corresponding probability using the normal probability table in the appendix. P(Z < 1.71) is given in the row starding 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)
=1  P(Z < 1.71)
=1  0.9564
=0.0436
=4.36% Thus about 4.36% of the 15-year-old students at this scool are expected to be taller than 180 cm.

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