Questions: The time it takes a person to wash the dishes is uniformly distributed between 12 minutes and 21 minutes. What is the probability that a randomly selected event of washing dishes will take a person between 15 and 17 minutes? Round your answer accurate to two decimal places.

Solution Steps

The total range of time for the event is calculated as $b - a = 21 - 12 = 9.$

The range of the specific time interval of interest is calculated as $d - c = 17 - 15 = 2.$

The probability that the event will have a duration within the specific time interval $[c, d]$ is given by the ratio of the range of the specific time interval to the total range of time. Therefore, the probability $P$ can be calculated as $P = \frac{d - c}{b - a} = \frac{2}{9} = 0.222.$ After rounding to 2 decimal places, $P = 0.22.$

Final Answer: