Chapter 2.1, Problem 9E

(a)

To determine

Whether the sprint time of 8 seconds usually slow.

Answer to Problem 9E

Sprint time of 8 seconds is not usually slow.

Explanation of Solution

Given information:

  

Calculations:

First

Draw the vertical line intersecting the horizontal axis at 8.

Then

Draw the horizontal line through the intersection of curve and vertical line.

Note that

Horizontal line roughly intersecting the axis at 73.

That implies

Around 73% of the students ran the 50 yards in less than 8 seconds.

And

The rest 27% of the students ran the 50 yards in more than 8 seconds.

Since

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

Thus,

The sprint time of 8 seconds is not usually slow, because 27% cannot be considered as small.

  

(b)

To determine

Interpretation of 20^th percentile of the distribution.

Answer to Problem 9E

Around 20% of the students sprint the 50 yards in less than 6.75 seconds.

Explanation of Solution

Given information:

  

Calculations:

The data value represented by the x^th percentile has x% of the data values below it.

That implies

The data value represented by the 20^th percentile has 20% of the data values below it.

Now,

Draw the horizontal line intersecting the vertical axis at 20.

Then

Draw the vertical line through the intersection of curve and horizontal line.

Note that

Vertical line roughly intersecting the horizontal axis at 6.75.

That implies

The 20^th percentile is roughly at 6.75 seconds.

Thus,

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