Final answer:
While the question seeks to find the expected weight of a 38-inch kindergartener, the actual data needed to find the line of best fit is not provided, hence the answer cannot be determined. Z-scores can calculate how far a value is from the mean in a normally distributed data set.
Step-by-step explanation:
The question asks for the determination of the expected weight of a 38-inch kindergartener using a line of best fit, given the heights and weights of a group of kindergartners. To answer this question, a graphing calculator is usually used to calculate the linear regression and find the line of best fit when height is the independent variable. After finding the equation, you would input the height of 38 inches to predict the corresponding weight. However, since we are not provided with actual data to calculate the line of best fit, the answer cannot be determined from the information given.
Z-scores are a measure that describe a value's relationship to the mean of a group of values, measured in terms of standard deviations from the mean. The given weights (11 kg, 7.9 kg, 12.2 kg) can be used to calculate their respective z-scores since we have the mean (μ = 10.2 kg) and the standard deviation (σ = 0.8 kg) for the reference population of 80 cm girls. The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation, like so: z = (X - μ) / σ.