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The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 16 and 17 minutes? Give your answer accurate to two decimal places. ?

Ask by Rogers Huang. in the United States
Feb 27,2025

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Answer

The probability is approximately 0.14 (14%).

Solution

The washing time is uniformly distributed between 11 and 18 minutes, so every minute within that range is equally likely. The total interval length is 18 - 11 = 7 minutes. The probability that the washing takes between 16 and 17 minutes is the length of that subinterval (1 minute) divided by the total interval length. Thus: Probability = (17 - 16) / 7 ≈ 1/7 ≈ 0.14 So, the probability is approximately 0.14 (or 14%).

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The Deep Dive

To find the probability that washing dishes will take between 16 and 17 minutes, we first determine the total range of time, which is 18 - 11 = 7 minutes. Since the distribution is uniform, the probability is calculated as the width of the interval of interest divided by the total range. The interval from 16 to 17 minutes is 1 minute wide. Therefore, the probability is: \[ P(16 \leq T \leq 17) = \frac{1}{7} \approx 0.142857 \] Rounding this to two decimal places gives us a probability of 0.14.

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