Questions: The time it takes me to wash the dishes is uniformly distributed between 7 minutes and 17 minutes. What is the probability that washing dishes tonight will take me between 14 and 16 minutes? Give your answer accurate to two decimal places.

Solution Steps

The time it takes to wash the dishes is uniformly distributed between \( a = 7 \) minutes and \( b = 17 \) minutes. The width of the distribution is given by:

\[ \text{scale} = b - a = 17 - 7 = 10 \]

The cumulative distribution function (CDF) at \( x = 16 \) is calculated as follows:

\[ P(X \leq 16) = 0.9 \]

The cumulative distribution function (CDF) at \( x = 14 \) is calculated as follows:

\[ P(X \leq 14) = 0.7 \]

The probability that washing dishes will take between 14 and 16 minutes is given by the difference of the two CDF values:

\[ P(14 < X < 16) = P(X \leq 16) - P(X \leq 14) = 0.9 - 0.7 = 0.2 \]

Final Answer