The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 16 minutes.

What is the probability that washing dishes tonight will take me between 13 and 15 minutes?

let m be the mean, and

let s be the standard deviation

(11 - m)/s = -3
11-m = -3s

(16-m)/s = 3
16-m = 3s

add them : 27 - 2m=0
m = 13.5
3s = 16-13.5 = 2.5

Using my favourite normal distribution calculator:
http://davidmlane.com/hyperstat/z_table.html

I get .305

To calculate the probability of washing dishes taking between 13 and 15 minutes, we first need to find the range of the uniform distribution.

The range of a uniform distribution is calculated by subtracting the minimum value from the maximum value.

In this case, the minimum value is 11 minutes and the maximum value is 16 minutes.

Range = Maximum value - Minimum value
Range = 16 minutes - 11 minutes
Range = 5 minutes

Now we need to find the width of the desired interval (between 13 and 15 minutes).

Width = Upper bound - Lower bound
Width = 15 minutes - 13 minutes
Width = 2 minutes

Finally, we can calculate the probability of the dishwashing time falling between 13 and 15 minutes by dividing the width of the interval (2 minutes) by the range of the distribution (5 minutes).

Probability = Width / Range
Probability = 2 minutes / 5 minutes
Probability = 0.4 or 40%

Therefore, the probability of washing the dishes tonight taking between 13 and 15 minutes is 40%.