# Lesson 6

Areas in Histograms

- Let’s find proportions of data in certain intervals.

### Problem 1

A normal curve with a mean of 500 and a standard deviation of 100 is shown. Shade the region under the curve within one standard deviation of the mean. How much of the data falls within the shaded region?

### Problem 2

The stopping distance of a certain car traveling at 60 miles per hour follows an approximately normal distribution with a mean of 130 feet and a standard deviation of 5 feet. Approximately what percent of the time does the car stop at a distance of between 120 feet and 140 feet?

### Problem 3

The distribution of weights for bags of chips is shown to follow an approximately normal distribution as seen in this histogram.

- What is the approximate mean weight of a chip bag?
- What is the approximate standard deviation of the weight of a chip bag?

### Problem 4

Here is a histogram of a distribution with 50 data points.

- 80 to 81
- 83 to 84
- 88 to 89

### Problem 5

Two curves representing normal distributions are shown. Does the solid curve or dashed curve have a greater standard deviation? Explain how you know.

### Problem 6

Why is it important to randomly assign people to random groups in an experimental study?