Do you carpool? Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows.x 1 2 3 4 5Px 0.65 0.20 0.10 0.03 0.02Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Compute the mean μX. Round the answer to three decimal places as needed.
Question
Do you carpool? Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows.x 1 2 3 4 5Px 0.65 0.20 0.10 0.03 0.02Part: 0 / 30 of 3 Parts CompletePart 1 of 3(a) Compute the mean μX. Round the answer to three decimal places as needed.
Solution
To compute the mean (μX), you need to multiply each value of X by its corresponding probability and then sum up these products. This is also known as the expected value of a probability distribution.
Here's how you do it:
μX = Σ [x * P(x)]
= (10.65) + (20.20) + (30.10) + (40.03) + (5*0.02)
= 0.65 + 0.40 + 0.30 + 0.12 + 0.10
= 1.57
So, the mean number of occupants in a randomly chosen car on this stretch of highway during morning commute hours is approximately 1.57.
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