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.

Greater than 3.00 minutes

<IMAGE>

Greater than 3.00 minutes

Accepted Answer

Welcome back, everyone. The figure below shows a 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 greater than 6 minutes? A says 0.2, B 0.4, C 0.6, and D 0.8. For this problem we're dealing with a continuous uniform distribution. So we want to identify the probability that our random variable, which is waiting time and minutes. X is greater than 6. Now, how do we do that? Well, essentially we can use the image on the screen. And what we're going to do is simply label X of 6 on the horizontal axis. Anything above 6 satisfies. The condition that the waiting time is greater than 6 minutes, right? So, above 6 minutes basically means that we're looking at the area to the right of 6, those could be 6789, or 10 minutes, right? So how do we find this probability? Well, essentially we need to identify the length of the interval and multiply it by the height of the. By the height of the whole distribution, right? So our length is the difference between 10 and 6. That'd be 10 minus 6. And our height is constant in this case, right? Specifically, we have a height which corresponds to 0.1 because we're taking the upper value 0.1, and we're subtracting the lower value, which is 0. So we end up with 4 multiplied by. 0.1, which gives us 0.4, and therefore, the correct answer to this problem corresponds to the answer choice B. Thank you for watching.

��app