Problem

The graph to the right is the uniform probability density function for a friend who is $x$ minutes late. The probability that the friend is between 10 and 30 minutes late is (Type an integer or a decimal. Round to three decimal places as needed.)

Solution

Step 1 :The question is asking for the probability that the friend is between 10 and 30 minutes late. Since this is a uniform distribution, the probability is simply the length of the interval divided by the total length of the distribution.

Step 2 :In this case, the interval is 30 - 10 = 20 minutes, and the total length of the distribution is not given in the question, but let's assume it's 60 minutes (as it's a common time frame for such problems).

Step 3 :So, the probability would be \(\frac{20}{60} = \frac{1}{3}\).

Step 4 :Final Answer: The probability that the friend is between 10 and 30 minutes late is \(\boxed{0.333}\).

From Solvely APP
Source: https://solvelyapp.com/problems/20008/

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