/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 9. Run fast! As part of a student p... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Big sharks Here are the lengths (in feet) of 44 great white sharks:

A dot plot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer based on the graph and the 68–95–99.7 rule.

nMeanSDMinQ1MedQ3Max
44155862.559.413.5515.7517.222.8

Are body weights Normal? The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. How about body weights? The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2pounds. The first and third quartiles are 118.3 pounds and 157.3pounds. Is it reasonable to believe that the distribution of body weights for women aged 20to 29 is approximately Normal? Explain

your answer.

Sudoku Mrs. Starnes enjoys doing Sudoku puzzles. The time she takes to complete an easy puzzle can be modeled by a Normal distribution with a mean of 5.3 minutes and a standard deviation of 0.9 minutes.

a. What proportion of the time does Mrs. Starnes finish an easy Sudoku puzzle in less than 3 minutes?

b. How often does it take Mrs. Starnes more than 6 minutes to complete an easy puzzle?

c. What percent of easy Sudoku puzzles take Mrs. Starnes between 6 and 8 minutes to complete?

A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams. Based on this report, what is the approximate standard deviation of weight for this species of cockroaches?

a.4.6b.5.0c.6.2d.14.0

e. Cannot determine without more information.

Multiple choice: Select the best answer. Mark receives a score report detailing his performance on a statewide test. On the math section, Mark earned a raw score of 39, which placed him at the 68th percentile. This means that

(a) Mark did better than about 39% of the students who took the test.

(b) Mark did worse than about 39% of the students who took the test.

(c) Mark did better than about 68%of the students who took the test.

(d) Mark did worse than about 68% of the students who took the test.

(e) Mark got fewer than half of the questions correct on this test.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.