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Chapter 1: Q21E (page 27)

The article cited in Exercise 20 also gave the following values of the variables y=number of culs-de-sac and z=number of intersections:

y

1

0

1

0

0

2

0

1

1

1

2

1

0

0

1

1

0

1

1

z

1

8

6

1

1

5

3

0

0

4

4

0

0

1

2

1

4

0

4

y

1

1

0

0

0

1

1

2

0

1

2

2

1

1

0

2

1

1

0

z

0

3

0

1

1

0

1

3

2

4

6

6

0

1

1

8

3

3

5

y

1

5

0

3

0

1

1

0

0

z

0

5

2

3

1

0

0

0

3

a. Construct a histogram for the ydata. What proportion of these subdivisions had no culs-de-sac? At least one cul-de-sac?

Short Answer

Expert verified

a.

The histogram is represented as,

Theproportion ofsubdivisions that had no culs-de-sac is 0.362.

The proportion of subdivisions that had at least oneculs-de-sac is 0.638.

Step by step solution

01

Given information

It is given that y represents the number of culs-de-sac and z represents the number of interactions.

02

Construct a histogram.

a.

The total number of culs-de-sac is 47.

The relative frequency is computed as,

\({\rm{relative frequency }} = \frac{{frequency}}{{Total\;number\;of\;observations}}\)

The table representing the relative frequency is computed as,

y

Frequency

Relative frequency

0

17

0.362

1

22

0.468

2

6

0.128

3

1

0.021

4

0

0.000

5

1

0.021

Steps to construct a histogram are,

1) Determine the frequency or the relative frequency.

2) Mark the class boundaries on the horizontal axis.

3) Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.

The histogram is represented as,

03

Compute the proportion

The proportionof subdivisions that had no culs-de-sac is computed as,

\(P\left( {y = 0} \right) = 0.362\)

Therefore, theproportion ofsubdivisions that had no culs-de-sac is 0.362.

The proportionof subdivisions that had at least one culs-de-sac is computed as,

\(\begin{aligned}P\left( {y \ge 1} \right) &= 1 - P\left( {y = 0} \right)\\ &= 1 - 0.362\\ &= 0.638\end{aligned}\)

Therefore, the proportion of subdivisions that had at least one culs-de-sac is 0.638.

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