Question

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

Answer 1

The probability from 1.5 ≤ x ≤ 3 can be calculated by dividing the Area from x=1.5 to x=3 by the total Area of the distribution. 

The given distribution is rectangular shaped, so its Area will be = Length x Width = 1 x 3 = 3 square units

From x = 1.5 to x = 3, the length is 1.5 and width is 1. So the area between these two intervals = 1.5 square units.

Thus, P(1.5 ≤ X ≤ 3) = 1.5/3 = 0.5

Answer 2

By calculating the area under the curve, we will see that:

P(1.5 ≤ X ≤ 3) = 0.5

How to get the probability?

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

If you want to learn more about probability, you can read:

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