# The time it takes to wash the dishes is uniformly distributed between 7 mins and 17 mins. ?

What is the probability that washing dishes tonight will take her between 10 and 15 mins?

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• The probability of washing the dishes per minute, p say, remains constant.

We can visualise a flat topped distribution of height p and width 17 – 7 = 10.

The key idea, (first noted by rotchm), is that the whole probability of washing

between 7 and 17 mins is 1; and that is represented by the rectangular area under graph, so, 10p = 1

We are asked about the probability that washing dishes tonight will take between 10 and 15 mins which amounts to 5p

That probability is 0.5

• uniformly distributed means that the prob at every instant is the same, hence constant "k".  Its graph is thus a constant from x=7 to 17. Sketch it to better see it.

Notice it makes a rectangle from 7 to 17 and of height "k".

Ita area is thus 10 x k = 10k. Since the whole prob (area under graph, or the rectangle) is 1 we then have 10k = 1 thus k = 1/10. So your graph is a constant of height 1/10.

Now locate x = 10 & 15. What is the area generated by this? that's your answer.

Another way to attain this result is the ratio (15-10) / (17 - 7). Does it give the same result?

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.

Dont forget to vote me best answer for being the first to correctly walk you through and especially for not spoiling out the answer!