Question

Consider a continuous random variable x, which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________.

Answer 1

We will see that the probability of x taking on a value between 75 to 90 is P = 0.5

How to get the probability?

We know that x is a continuous random variable uniformly distributed between 65 and 85.

This means that the probability that x value y in the range is such that:

1 = P(y)*(85 - 65) = P(y)*20

1/20 = P(y).

Now, the probability of x taking a value between 75 and 85 is:

P(75 to 85) = (1/20)*(85 - 75) = 10/20 = 0.5

And the probability between 85 and 90 is zero (because the maximum value that x can take is 85, so this part does not affect).

Then we conclude that the probability of x taking a value between 75 to 90 is:

P(75 to 90) = P(75 to 85) + P(85 to 90) = 0.5 + 0 = 0.5

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

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