Predicting Population Percentages Using a Graphing Calculator

This lesson teaches how to predict population percentages using a graphing calculator. It reviews the normal model, emphasizing the need to check data distribution before applying it. The empirical rule is explained, highlighting its limitations. A practical example using milk jugs demonstrates how to use a graphing calculator to find percentages under a normal distribution. The lesson also covers different methods for determining probabilities and provides detailed instructions for using a graphing calculator's statistics functions.

What must be checked before applying the normal model to a data set?

• The data set must have outliers and not follow the empirical rule.

• The data set must be multi-peaked and asymmetric.

• The data set must be single-peaked, symmetric, have no outliers, and follow the empirical rule.

• The data set must be skewed and have multiple modes.

Why is it important to continue sketching graphs even when using a graphing calculator?

• Sketching helps in visualizing the problem and guiding your thinking.

• Sketching graphs is only important for non-normal distributions.

• Sketching is not necessary if you have a graphing calculator.

• Sketching is only required for empirical rule applications.

In the milk jug example, why can't the empirical rule be used to find the percentage of jugs with less than 63.5 ounces?

• Because 63.5 ounces is a fraction of one full standard deviation from the mean.

• Because the standard deviation is not 8/10 of an ounce.

• Because the mean is not 64 ounces.

• Because 63.5 ounces is exactly one standard deviation from the mean.

Which of the following is NOT a method to determine probabilities from a normal distribution?

• Empirical rule

• Random guessing

• Graphing calculator statistics functionality

• Standard normal table and z-scores

What is the first step in using a graphing calculator to find a percentage under the normal curve?

• Calculate the z-score manually.

• Input the mean and standard deviation.

• Select the Normal CDF function from the Distributions menu.

• Draw a sketch of the normal curve.

What values are required to use the Normal CDF function on a graphing calculator?

• Only the mean and the lower bound.

• Only the mean and standard deviation.

• The lower and upper bounds, mean, and standard deviation.

• Only the lower and upper bounds.

What is the approximate percentage of jugs that will need to be refilled if they contain less than 63.5 ounces?

• 16%

• 50%

• 27%

• 63%