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Run fast! As part of a student project, high school students were asked to

sprint 50 yards and their times (in seconds) were recorded. A cumulative relative frequency graph of the sprint times is shown here.

a. One student ran the 50 yards in 8 seconds. Is a sprint time of 8 seconds unusually slow?

b. Estimate and interpret the 20th percentile of the distribution.

Short Answer

Expert verified

Part (a) Sprint time of 8 seconds is not usually slow.

Part (b) Around 20% of the students sprint the 50 yards in less than 6.75 seconds.

Step by step solution

01

Part (a) Step 1: Given information

The figure is

02

Part (a) Step 2: Concept

The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.

03

Part (a) Step 3: Explanation

First

At 8, draw a vertical line that intersects the horizontal axis.

Then

Draw a horizontal line through the point where the curve and the vertical line intersect.

Note that

The horizontal line roughly intersects the axis at 73

That implies

Around 73 percent of the children completed the 50-yard dash in under eight seconds.

And

The remaining 27% of pupils ran the 50-yard dash in under 8 seconds.

Since

A percentage less than 5% is considered to be small.

Thus,

Because 27 percent cannot be deemed little, an 8-second sprint time is not considered slow.

04

Part (b) Step 1: Explanation

The xth percentile represents a data value with x percent of the data values below it.

That implies

The 20th percentile represents a data value with 20% of the data values below it.

Now,

Draw the horizontal line intersecting the vertical axis at 20

Then

Draw a vertical line through the curve and the horizontal line's intersection.

Note that the vertical line roughly intersects the horizontal axis at 6.75

That implies

The 20th percentile is roughly at 6.75 seconds.

Thus,

In less than 6.75 seconds, around 20% of all the students sprint 50 yards.

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