Answer:
The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.
Step-by-step explanation:
Let the random variable <em>X</em> represent the time it takes to wash the dishes.
The random variable <em>X</em> is uniformly distributed with parameters <em>a</em> = 10 minutes and <em>b</em> = 15 minutes.
The probability density function of <em>X</em> is as follows:

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

![=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B5%7D%5Cint%5Climits%5E%7B12%7D_%7B14%7D%20%7B1%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%5Ctimes%20%5Bx%5D%5E%7B14%7D_%7B12%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B15%7D%5Ctimes%20%5B14-12%5D%5C%5C%5C%5C%3D%5Cfrac%7B2%7D%7B15%7D%5C%5C%5C%5C%3D0.1333)
Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.