Question

the graph represents the distribution of the lengths of play times, in minutes, for songs played by a radio station over one hour. which statement is true about the songs played during the one - hour interval? most of the songs were between 3 minutes and 3.8 minutes long. most of the songs were 3.4 minutes long. most of the songs were less than 3.2 minutes long. most of the songs were more than 3.6 minutes long.

Explanation:

Step1: Analyze the graph

The graph is a normal - like distribution. In a distribution graph, the area under the curve represents the proportion of data. The highest point of the curve (mode - like region for non - discrete data) and the regions around it have a relatively large area.

Step2: Evaluate each option

• Option 1:

The region between \(3\) and \(3.8\) minutes has a large area under the curve. Since the area under the curve of a distribution graph (where the \(x\) - axis is the song length and the \(y\) - axis is related to the frequency density) represents the proportion of songs, a large area in the \(3 - 3.8\) minute interval means a large proportion of songs.

• Option 2:

A single value (\(3.4\) minutes) in a continuous distribution (song lengths can be any value in a range) does not represent “most” of the data. The graph is for a continuous variable (song length in minutes), and we are interested in intervals, not single - point values.

• Option 3:

The area of the region where \(x<3.2\) is much smaller than the area of the region \(3 < x<3.8\).

• Option 4:

The area of the region where \(x > 3.6\) is much smaller than the area of the region \(3 < x<3.8\).

Answer:

Most of the songs were between 3 minutes and 3.8 minutes long.