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Chapter 2: Q 73. (page 141)

Normal highway driving? The dot plot shows the EPA highway gas mileage estimates in miles per gallon (mpg) for a random sample of 21 the model year 2018 midsize cars.11 Explain why this distribution of highway gas mileage is not approximately Normal.

Short Answer

Expert verified

The distribution has been skewed to the right instead of roughly symmetric.

Step by step solution

01

Given information

02

Concept

A dot plot is a graphical display of data using dots.

03

Explanation

The symmetric nature of the Normal distribution is one of its characteristics.

The distribution in the dot plot is skewed to the right; we can also see that most of the dots in the dot plot are to the left, with a tail of less common values to the right.

We know that

The Normal distribution should be symmetric.

And

The distribution is biased to the right in this case.

We can say

This distribution is not approximately the Normal distribution.

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Most popular questions from this chapter

Flight times An airline flies the same route at the same time each day. The flight time varies according to a Normal distribution with unknown mean and standard deviation. On 15% of days, the flight takes more than an hour. On 3% of days, the flight lasts 75 minutes or more. Use this information to determine the mean and standard deviation of the flight time distribution.

Teacher raises A school system employs teachers at salaries between \(38,000 and Page Number: 107\)70,000 The teachers’ union and school board are negotiating the form of next year’s increase in the salary schedule. Suppose that every teacher is given a $1000 raise. What effect will these raises have on each of the following characteristics of the resulting distribution of salary?

a. Shape

b. Mean and median

c. Standard deviation and interquartile range (IQR)

Refrigerators Consumer Reports magazine collected data on the usable

capacity (in cubic feet) of a sample of 36 side-by-side refrigerators. Here are the data:

A histogram of the data and summary statistics are shown here. Is this distribution of refrigerator capacities approximately Normal? Justify your answer based on the graph and the 68–95–99.7 rule.

Don’t call me According to a study by Nielsen Mobile, “Teenagers ages 13 to 17 are by far the most prolific texters, sending 1742 messages a month.” Mr. Williams, a high school statistics teacher, was skeptical about the claims in the article. So he collected data from his first-period statistics class on the number of text messages they had sent over the past 24 hours. Here are the data:

a. Sunny was the student who sent 42 text messages. What is Sunny’s percentile?

b. Find the number of text messages sent by Joelle, who is at the 16th percentile of the distribution.

I think I can! An important measure of the performance of a locomotive is its “adhesion,” which is the locomotive’s pulling force as a multiple of its weight. The adhesion of one 4400-horsepower diesel locomotive varies in actual use according to a Normal distribution with mean μ=0.37and standard deviation .σ=0.04For each part that follows, sketch and shade an appropriate Normal distribution. Then show your work.

(a) For a certain small train’s daily route, the locomotive needs to have an adhesion of at least 0.30for the train to arrive at its destination on time. On what proportion of days will this happen? Show your method.

(b) An adhesion greater than 0.50for the locomotive will result in a problem because the train will arrive too early at a switch point along the route. On what proportion of days will this happen? Show your method.

(c) Compare your answers to (a) and (b). Does it make sense to try to make one of these values larger than the other? Why or why not?
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