Chapter 2.1, Problem 27E

(a)

To determine

To explain: the reason for which satisfies the two requirementsfor a density curve.

Answer to Problem 27E

As the curve is on or above the horizontal axis everywhere, and it forms a density of $\frac{1}{3}by3$ rectangles: therefore, the area beneath the curve is 1.

Explanation of Solution

Given:

  

As the curve is on or above the horizontal axis everywhere, and it forms a density of $\frac{1}{3}by3$ rectangles: therefore, the area beneath the curve is 1.

  

Therefore the given curve satisfies the two requirements of density curve.

(b)

To determine

To find: this area

Answer to Problem 27E

Explanation of Solution

Calculation:

From the given density curve, we observe that one-third of accidents occur in the first mile:that means $\frac{1}{3}by1$ rectangle bounded between 0 miles and 1 mile. Therefore, the proportion of accidents that occur in the first mile of the path is $\frac{1}{3}$ .

  

Conclusion:

Therefore, the proportion of accidents that occur in the first mile of the path is $\frac{1}{3}$ .

(c)

To determine

To find: proportion of accidents happen in front of S’s property

Answer to Problem 27E

The proportion of accidents happen in front of Sue's property is $0.1$

Explanation of Solution

Calculation:

Here we have informed that Sue's property adjoins the bike path between 0.8 mile mark andthe 1.1 mile mark. That means, the distance between his properties is given as 0.3 miles.

By definitions, the proportion of accidents happen in front of Sue's property is one-third of 0.3miles.

  

The proportion of accidents happen in front of Sue's property is $0.1$

Conclusion:

Therefore, the proportion of accidents happen in front of Sue's property is $0.1$