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 $P(x <= a) = 0.14$ true?

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Answer 1 · 2017-11-24T12:18:51

$a=1.7$

The diagram below show the uniform distribution for the given range
enter image source here

the rectangle has area $=1$

so $(6-1)k=1$

$=>k=1/5$

we want $P(X<=a)=0.14$

this is indicated as the grey shaded area on the diagram

so:

$(a-1)k=0.14$

$(a-1)xx1/5=0.14$

$a-1=0.14xx5=0.7$

$:.a=1.7$

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) = 0.14P(x <= a) = 0.14 true?