Suppose a random variable $x$ $x$ is best described by a uniform probability distribution with range 1 to 6. What is the value of $a$ $a$ that makes $P (x \leq a) = 0.14$ $P(x <= a) = 0.14$ true?

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Answer 1 · 2017-11-24T12:18:51

$a = 1.7$ $a=1.7$

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

the rectangle has area $= 1$ $=1$

so $(6 - 1) k = 1$ $(6-1)k=1$

$\Rightarrow k = \frac{1}{5}$ $=>k=1/5$

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

this is indicated as the grey shaded area on the diagram

so:

$(a - 1) k = 0.14$ $(a-1)k=0.14$

$(a - 1) \times \frac{1}{5} = 0.14$ $(a-1)xx1/5=0.14$

$a - 1 = 0.14 \times 5 = 0.7$ $a-1=0.14xx5=0.7$

$:.a=1.7$

Suppose a random variable xxx is best described by a uniform probability distribution with range 1 to 6. What is the value of aaa that makes P(x <= a) = 0.14P(x≤a)=0.14P(x <= a) = 0.14 true?