Question

1/ Assume that the distribution of residuals is approximately normal with mean 0 cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer.
2/ Base on your answer on part 1, would it be surprising to randomly select a high school senior from the high school with a foot length of 20cm and a height greater than 165cm? Justify your answer.

Answer 1

Answer:

1. 8.576%

2. Yes

Step-by-step explanation:

1. Use the calculator

Enter: normalcdf(8, E99, 0, 5.9)

This is equal to .08756.

Convert this number into a percent = 8.756%

2.

First, calculate the residual

Residual = Observed - Predicted = 165 - 2.599(20) + 105.08 = 7.94

Use the calculator

Enter: normalcdf(7.94, E99, 0, 5.9)

This is equal to .0892.

Convert this number into a percent = 8.92%

This would be surprising, because the chance of this happening is very low.