# Chapter 1. Normal Density Curve

## Introduction

Statistical Applets

The applet calculates the area shaded dark yellow under the curve. To find the proportion of values less than a given value, drag the left flag to that value. Similarly, to find the proportion of values greater than a given value, drag the right flag to that value. For the proportion between two values, drag the right flag to the smaller value, and the left flag to the larger value.

Click the "Quiz Me" button to complete the activity.

The mean and standard deviation (std. dev.) characterize the normal density curve. The mean is the center point of the density curve. In the applet below, four std. dev. to the left and to the right of the mean are marked on the graph axis. To change these parameters type in the desired value(s) and press the UPDATE button. By default the mean is set equal to 0 and the std. dev. is set equal to 1 (i.e., "Standard Normal Density").

The curve tails are delimited by the two vertical green flags. The tail values can be set by clicking on a flag and dragging. Notice that a flag's value is displayed at the top of each flag. If the 2-Tail checkbox is checked the tails are locked symmetrically around the mean.

3
Correct.
Try again.
Incorrect.

3
Correct.
Try again.
Incorrect.

### Question 1.3

Suppose you know that the amount of time it takes your friend Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. Use the applet to answer the questions below.

• What proportion of Susan's trips to class would take more than 50 minutes? (Hint: you should not need to use the applet to know this value) uJISCg90RZk=
• What proportion of Susan's trips to class would less than 40 minutes? pm8f93oFmjs=
• What proportion of Susan's trips to class would take more than 50 minutes or less than 40 minutes? 4Dm6tl/E7rY=

3
Try again.
Incorrect. See above for the correct answers.
Great job.
Various calculations using the applet

### Question 1.4

LSUE6AxOUrLEs3oFVOjlCq9qsII9LVfBAppTTUbL1PmTogQCgh/2dw1xyyx4mZROztYiZ4cts9RY1F9KTlMab74dyitGgbYUSSbj4MnZ0i3Khv9Gp7xXMYcPf7ud2fl9JYDjfoBrxr2minXKgQFkwEOU7EhBFaMFrP7TPebyB2IEI1TfFqRqMFmCUeMf90XcE9otisnNbst6o/sHy3kOs6iNQp0arlkrfu8aAJdVO7cOw5X0znu30+zOApmenPM4vI7de8WBdjbLuDGY5NhP0e1GBtwWePIBaSytcVX6sytlOr7jfr0nfLTzXXQ+A3sSRjI2yzvD0HKkLtOOx26eeWJ/doRrvdcpAnP9b1H9fT33IFzRgJbEPw==
3
Correct.
Try again.
Incorrect.