Question

The probability density of a random variable X is given in the figure below. From this density, the probability that X is at least 0.48 is: .Give your answer to at least 4 decimal places.

Answer 1

X is a value between 0 and 2. We want to find the probability of x ≥ 0.48. Those numbers are the numbers between 0.48 and 2.

Thus:

`2-0.48=1.52`

Now, we calculate the probability, 1.52 is the favorable outcomes and 2 is the total outcomes:

`P(x\ge0.48)=(1.52)/(2)=0.76`

The probability in decimal is 0.76

The probability in fraction form is:

`(19)/(25)`

And the probability as a percentage is:

`0.76\cdot100=76\%`