Question

The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 14 minutes. What is the probability that washing dishes tonight will take me between 9 and 12 minutes? Give your answer accurate to two decimal places.

Answer 1

50% probability that washing dishes tonight will take me between 9 and 12 minutes

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d, d greater than c, is given by the following formula.

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

The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 14 minutes.

This means that
`a = 8, b = 14`

What is the probability that washing dishes tonight will take me between 9 and 12 minutes?

`P(9 \leq X \leq 12) = (12 - 9)/(14 - 8) = 0.5`

50% probability that washing dishes tonight will take me between 9 and 12 minutes