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#