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8 Nov 2021
Given information
Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months ( years) to years.
Find the third quartile of ages of cars in the lot. This means you will have to find the value such that , or , of the cars are at most (less than or equal to) that age.
Step-by-step explanation
Step 1.
We know is the notation for uniform distribution. Where, is the lowest value of and is the highest value of .
The probability density function is as follows:
where .
According to the given information, the distribution of is uniform with parameters and , in mathematical terms
Substituting , we get
where .
It is given that
The third quartile means 75% of the cars are at most (less than or equal to) that age, symbolically, The base of the rectangle is
Therefore,
,
Therefore, the third quartile is .
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