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#