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?
- Ian HLv 73 months ago
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
- rotchmLv 73 months ago
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?
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