The function g(x) is a transformation of the cube root parent function, f(x) = y. What function is g(x)?

Step-by-step explanation:

a) According to the least-squares regression line, the estimated height for a high school senior with a foot length of 20 cm is:

y = 2.599x + 105.08

y = 2.599(20) + 105.08

y = 157.06

The residual is 160 − 157.06 = 2.94

b) The differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.

c) Calculate the z-score:

z = (x − μ) / σ

z = (8 − 0) / 5.9

z = 1.36

Use a calculator or table to find the probability.

P(Z > 1.36) = 1 − 0.9131 = 0.0869

Therefore, approximately 8.69% of the residuals are larger than 8 cm.

d) Since the z-score is within ±2 standard deviations, it would not be surprising to randomly select a high school senior with a foot length of 20 cm and height of 165 cm.