Continuous Uniform Distribution. In Exercises 5–8, refer to th...

Question

Continuous Uniform Distribution. In Exercises 5–8, 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

Less than 4.00 minutes

Accepted Answer

Welcome back, everyone. The figure below shows the continuous uniform distribution of customer waiting times at a coffee shop. If a customer is randomly selected, what is the probability that their waiting time is less than 8 minutes? A says 0.8, B 0.6, C 0.4, and D 0.2. In this problem, we're dealing with a continuous uniform distribution. We want to identify the probability that the waiting time is less than 8 minutes, and according to the given sketch, it is our random variable X. So we want to identify the probability that X is less than 8. If we consider our sketch, we're going to draw a vertical line passing through X equals 8, and we have to understand that if X is less than 8, then we are interested. In the area to the left of 8, and now our probability for a uniform distribution is simply the ratio between the area that satisfies the condition. In this case, X must be less than 8, that'll be our A1, and the total area which is given as 1, right? We're going to call it ATA total. So now A1. The area of interest can be found by using the formula for the area of a rectangle. We have the length of the interval from 0 to 8, so that's 8. Multiplied by height. And height is 0.1, right? Because 0.1 minus 0 gives us 0.1, and the total area is given as 1. So we get 8 multiplied by 0.1 divided by 1, which is 0.8. Meaning the correct answer corresponds to the answer choice a. Thank you for watching.

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