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Chapter 2: Q. 5 (page 137)

What the mean means The figure below is a density curve. Trace the curve onto your paper.

(a) Mark the approximate location of the median. Justify your choice of location.

(b) Mark the approximate location of the mean. Justify your choice of location.

Use the 68-95-99.7 rule to estimate the percent of observations from a Normal distribution that fall in an interval involving points one, two, or three standard deviations on either side of the mean.

Short Answer

Expert verified

a. The median will be significantly to the right of the peak since it will be greater as the most common values grow..

b. Because the median is not affected by extremely large values as effectively as the mean, the mean also lies to the right of the median.

Step by step solution

01

Part(a) Step 1: Concept Introduction

To get the mean of a data set, divide by the number of values in it. The median is the point where the highest and lowest values meet.

02

Part(a) Step 2: Explanation

Because the tail of large values causes the median to grow as the most common values grow, the median will lie slightly to the right of the peak:

03

Part(b) Step 1: Concept Introduction

To get the mean of a data set, divide by the number of values in it. The median is the point where the highest and lowest values meet.

04

Part(b) Step 2: Explanation

Because the tail of large values causes the mean to become larger as the most common values, the mean will lie to the right of the peak.

Because the mean is influenced more strongly by extremely big numbers than the median, it is also to the right of the median.

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Most popular questions from this chapter

Weights aren鈥檛 Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. What can you say about the shape of the weight distribution? Why?

R2.12 Assessing Normality A Normal probability plot of a set of data is shown here. Would you say that these measurements are approximately Normally distributed? Why or why not?

R2.6 Horse pregnancies Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal

distribution with a mean of 336 days and a standard deviation of 3 days. Use the 68-95-99.7 rule to answer the following questions.

(a) Almost all (99.7%)horse pregnancies fall in what range of lengths?

(b) What percent of horse pregnancies are longer than 339 days? Show your work.

Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his

measurements is 0.2inches too large. Clarence鈥檚 data had a mean of 3.2inches and a standard deviation of 0.1 inches. Find the mean and standard deviation of the corrected measurements in centimeters (recall that 1 inch = 2.54 cm).

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''
See all solutions

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