/*! 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 10. Light it up! The graph below is ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Light it up! The graph below is a cumulative relative frequency graph showing the lifetimes (in hours) of 200 lamps.

(a) Estimate the 60th percentile of this distribution. Show your method.

(b) What is the percentile for a lamp that lasted 900 hours?

Short Answer

Expert verified

Part (a) 1000 is the estimate of the60th percentile of the lifetimes of 2000 lamps.

Part (b) A lamp that lasted900hours is at 35th percentile.

Step by step solution

01

Part (a) Step 1. Given

02

Part (a) Step 2. Concept

On a scale of 100, a score in the 95th percentile represents the percentage of a distribution that is equal to or below it.

03

Part (a) Step 3. Calculation

Step 1: Determine the place on the ogive where the line intersects the ogive by drawing a horizontal line from the value 60 on the vertical axis.

Step 2: From this point, draw a vertical line to the horizontal axis. At around 1000, the line intersects the axis. The 60th percentile of the lifespan of 2000 bulbs is estimated to be 1000 in the graph above. Therefore, 1000 is the estimate of the 60thpercentile of the lifetimes of 2000 lamps.

04

Part (b) Step 1. Explanation

Step 1: Determine the location on the ogive where the line intersects the ogive by drawing a vertical line from the value900 on the horizontal axis.

Step 2: From this point, draw a horizontal line to the vertical axis. At around 35, the line crosses the axis. A light that lasts 900 hours is in the 35th percentile, according to the graph above.

Therefore, a lamp that lasted 900 hours is at 35th percentile.

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

Potato chips The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with a mean μ=9.12ounces and standard deviation α=0.05ounce. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the points one, two, and three standard deviations away from the mean on the horizontal axis. Use rule68-95-99.7.

a) What percent of bags weigh less than 9.02ounces?

(b) Between what weights do the middle 68%of bags fall?

(c) What percent of 9-ounce bags of this brand of potato chips weigh between 8.97and 9.17ounces?

(d) A bag that weighs9.07 ounces is at what percentile in this distribution?

Each year, about 1.5million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was 46.9and the standard deviation was10.9. Nationally, 5.2%of test takers earned a score of 65 or higher on the Critical Reading test’s 20to 80scale.9

PSAT scores Scott was one of 50junior boys to take the PSAT at his school. He scored 64on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all 50boys’ Critical Reading scores, the mean was 58.2and the standard deviation was 9.4

(a) Write a sentence or two comparing Scott’s percentile among the national group of test-takers and among the 50boys at his school.

(b) Calculate and compare Scott’s z-score among these same two groups of test-takers.

T2.7. If the heights of American men follow a Normal distribution, and 99.7% have heights between 5'0'' and 7'0'', what is your estimate of the standard deviation of the height of American men?
(a) 1''
(b) 3''
(c) 4''
(d) 6''
(e) 12''

The distribution of heights of young women aged 18to 24is approximately N(64.5,2.5)

2. What percent of young women have heights greater than 67inches? Show your work.

Runners’ heart rates The figure below is a Normal probability plot of the heart rates of 200male runners after six minutes of exercise on a treadmill.14The distribution is close to Normal. How can you see this? Describe the nature of the small deviations from Normality that are visible in the plot.

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.