Distributions In a continuous uniform distribution,

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Question

Distributions In a continuous uniform distribution,

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a. Find the mean and standard deviation for the distribution of the waiting times represented in Figure 6-2, which accompanies Exercises 5–8.

Accepted Answer

Welcome back, everyone. The figure below shows the continuous uniform distribution of customer waiting times at a coffee shop. Determine the mean and standard deviation for the distribution of the waiting times. For this problem we're dealing with the continuous uniform distribution, and we have to recall that its mean is calculated as the sum of the end points A and B divided by 2 and the standard deviation. is equal to b minus a divided by square root of 12. We have to identify the A and B values. So A is the starting value on the horizontal axis, and that would be 0, right, because our distribution begins at 0. Therefore, A is 0, and B is the endpoint. Which is 10, right? That's the final value where our distribution ends. So now that we have A and B, we can identify the mean value. Which is A + B 0 + 10 divided by 2. Those would be in minutes, and that's 5 minutes. And now our standard deviation is equal to B minus A. 10 minus 0 divided by a square root of 12. And that's 10 divided by square root of 12, which is 2.9 minutes, we can also include the units. 2.9 minutes. Well then, so we have identified our mean and standard deviation for this problem. Thank you for watching.

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Distributions In a continuous uniform distribution,

a. Find the mean and standard deviation for the distribution of the waiting times represented in Figure 6-2, which accompanies Exercises 5–8.

Key Concepts

Continuous Uniform Distribution

Mean of a Uniform Distribution

Standard Deviation of a Uniform Distribution

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Distributions In a continuous uniform distribution,a. Find the mean and standard deviation for the distribution of the waiting times represented in Figure 6-2, which accompanies Exercises 5–8.