Suppose a random variable $x$ is best described by a uniform probability distribution with range 1 to 6. What is the value of $a$ that makes $P(x >= a) = 0.45$ true?

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Answer 1 · 2018-03-19T10:18:15

$a=3.75$

The uniform distribution can be visualized by the diagram below enter image source here

The area of the rectangle represents the probability. The total area in the interval $[1,6]$ must therefore equal $1$

$:. (6-1)k=1$

$=>k=1/5$

we want to find $a$ such that

$P(X>=a) =0.45$

so

$1/5(6-a)=0.45$

$6-a=0.45xx5=2.25$

$:.a=6-2.25=3.75$

Suppose a random variable xx is best described by a uniform probability distribution with range 1 to 6. What is the value of aa that makes P(x >= a) = 0.45P(x >= a) = 0.45 true?