The graph shows a probability distribution. What is P(1.5 ≤ X ≤ 3)? Enter your answer, as a decimal, in the box.

By calculating the area under the curve, we will see that:
P(1.5 ≤ X ≤ 3) = 0.5
We define P(1.5 ≤ X ≤ 3) as the probability of getting an outcome between 1.5 and 3, and this will be equal to the area under the curve bounded by these values.
We can see that the probability is a constant:
P(x) = k
for all the values between 1 and 4, so the "height" k will be such that:
k*3 = 1 (the total red area is equal to 1)
k = 1/3
then the area on the interval (1.5 ≤ X ≤ 3) is given by:
P = k*(3 - 1.5) = (1/3)*(3 - 1.5) = 1.5/3 = 0.5
Then we have:
P(1.5 ≤ X ≤ 3) = 0.5
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