Accidents on a Bike Path. Examining the location of accidents on a level. 8-mile bike path...
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Accidents on a Bike Path. Examining the location of accidents on a level. 8-mile bike path shows that they occur uniformly along the length of the path. Figure 3.4 displays the density curve that describes the distribution of accidents Height - 1/8 -- 1/16 -- 2. Distance along bike path (miles) FIGURE 3.4 The density curve for the location of accidents along an 8-mile bike path, for Exercise 3.2. (a) Explain why this curve satisfies the two requirements for a density curve. (b) The proportion of accidents that occur in the first 3 miles of the path is the area under the density curve between 0 miles and 3 miles. What is this area! (c) There is a stream alongside the bike path between the 1.5-mile mark and the 3.0-mile mark. What proportion of accidents happen on the bike path alongside the stream? (d) There are small towns at the two ends of the bike path, but the remainder of the paved bike path goes through the woods. What proportion of accidents occur more than 1 mile from either town? (Hint: First determine where on the bike path the accident needs to occur to be more than 1 mile from either town, and then find the area.) Accidents on a Bike Path. Examining the location of accidents on a level. 8-mile bike path shows that they occur uniformly along the length of the path. Figure 3.4 displays the density curve that describes the distribution of accidents Height - 1/8 -- 1/16 -- 2. Distance along bike path (miles) FIGURE 3.4 The density curve for the location of accidents along an 8-mile bike path, for Exercise 3.2. (a) Explain why this curve satisfies the two requirements for a density curve. (b) The proportion of accidents that occur in the first 3 miles of the path is the area under the density curve between 0 miles and 3 miles. What is this area! (c) There is a stream alongside the bike path between the 1.5-mile mark and the 3.0-mile mark. What proportion of accidents happen on the bike path alongside the stream? (d) There are small towns at the two ends of the bike path, but the remainder of the paved bike path goes through the woods. What proportion of accidents occur more than 1 mile from either town? (Hint: First determine where on the bike path the accident needs to occur to be more than 1 mile from either town, and then find the area.)
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