Normal CDF and Inverse Normal Functions

This video tutorial explains how to use graphing calculators to solve problems involving normal distributions. It covers the use of the normal CDF function to find the area under the curve and the inverse normal function to find percentiles. The tutorial includes practical examples, such as determining the percentage of milk jugs that overflow and finding the 95th percentile volume. It emphasizes the importance of understanding when to use each function and provides step-by-step instructions for using a graphing calculator.

What is the primary use of the normal CDF function on a graphing calculator?

• To plot a histogram

• To find the mean of a data set

• To calculate the standard deviation

• To determine the area under the normal curve between two values

In the milk jug example, what is the mean volume of milk per jug?

• 64.5 ounces

• 64 ounces

• 63.5 ounces

• 65 ounces

What percentage of jugs are expected to overflow if they are filled with more than 65 ounces?

• 11%

• 5%

• 20%

• 15%

What does the inverse normal function help you find?

• The mean of a distribution

• The total area under the curve

• The standard deviation of a distribution

• A threshold value for a given percentage

How does the inverse normal function interpret the area input?

• As the area under the curve from the right

• As the area under the curve from the left

• As the total area under the curve

• As the area above the curve

What is the 95th percentile volume for the milk jugs?

• 64 ounces

• 63.5 ounces

• 65.3 ounces

• 66 ounces

If you want to find a value that 72% of the jugs exceed, what percentile should you calculate?

• 72nd percentile

• 28th percentile

• 50th percentile

• 95th percentile

When should you use the normal CDF function?

• When you need to calculate the mean

• When you know the threshold and need the percentage

• When you know the percentage and need the threshold

• When you need to calculate the standard deviation

What is the result of using the inverse normal function with an area of 0.28?

• The standard deviation of the distribution

• A value that 72% of the data exceeds

• A value that 28% of the data exceeds

• The mean of the distribution

What is the key difference between normal CDF and inverse normal functions?

• Normal CDF is for plotting graphs, inverse normal for calculating areas

• Normal CDF finds percentages, inverse normal finds threshold values

• Normal CDF is used for discrete data, inverse normal for continuous data

• Normal CDF is used for calculating means, inverse normal for standard deviations