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Chapter 6: Q6 (page 240)

Continuous Uniform Distribution. In Exercises 5鈥�8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.


Less than 4.00 minutes

Short Answer

Expert verified

The probability for waiting time larger than 3.00 minutes is 0.4.

Step by step solution

01

Given information

The graph for a uniform distribution is given with an area enclosed equally to 1.

02

State the relationship between area and probability

When the area under the density curve is 1, it can be assured that there is a one-to-one relationship between area and probability.

The probability that the waiting time is less than 4.00 minutes would be the same as the area of the shaded region shown below.

03

Find the probability

The probability that the waiting time is lesser than 4.00 minutes is the area of a rectangle with length 0.2 and width is 4-0=4units.

Thus,

PX<4.00=Length脳widthoftheshadedarea=0.2脳4=0.8

Thus, the probability of selecting a passenger randomly when the waiting time is lesser than 4.00 minutes is 0.8.

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