Textbook ExpertVerified Tutor
2 Nov 2021
Given information
Use the following information to answer the next eight exercises. A distribution is given as
Step-by-step explanation
Step 1.
The notation of the uniform distribution is,
,
Where, is the lowest value of and is the highest value of .
The probability density function is as follows:
for .
According to the given information, the distribution of is uniform with parameters and , in mathematical terms
.
Substituting the values of and , we get
where .
The height of the distribution is .
Since, forty percent fall below the percentile, therefore
,
The base of the rectangle is .
The formula of the area of the rectangle is given by,
Substitute for base and for height in the above-mentioned formula.
The area of the rectangle is,
Therefore, the percentile is
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