Question

The time it takes me to wash the dishes is uniformly distributed between 12 minutes and 22 minutes.What is the probability that washing dishes tonight will take me between 18 and 21 minutes?Give your answer accurate to two decimal places.

Answer 1

When the probability is uniformly distributed it means that the events are equally likely to occur.

The lower limit of the distribution is 12 minutes (let's call it a) and the upper limit of the distribution is 22 minutes (let's call it b).

The probability of finding a value X between c (18 minutes) and d (21 minutes) is given by the following formula:

`P(c\le X\le d)=(d-c)/(b-a)`

By replacing the known values we obtain:

`\begin{gathered} P(18\le X\le21)=(21-18)/(22-12) \\ P(18\le X\le21)=(3)/(10) \\ P(18\le X\le21)=0.3 \end{gathered}`

The probability that washing dishes tonight will take me between 18 and 21 minutes is 0.3