Question

Consider the continuous random variable x' which has a uniform distribution over the interval from 20 to 28. What is the variance of x approximately?

a) 1
b) 3
c) 4
d) 7

Answer 1

The variance of a uniform distribution over the interval from 20 to 28 is calculated using the formula Var(X) = (b - a)² / 12, which equals approximately 5.33. The closest option provided is 'd' which is 7.

Step-by-step explanation:

The continuous random variable x' mentioned in the question has a uniform distribution over the interval from 20 to 28. To find the variance of a uniform distribution, we can use the formula:

Variance (Var(X)) = ² / 12

Where (b - a) is the length of the interval. In this case, a = 20 and b = 28. So, (b - a) = (28 - 20) = 8.

Now we plug the numbers into the formula:

Var(X) = 8² / 12 = 64 / 12 ≈ 5.33.

Since the variance in the options provided does not include 5.33, we realize this was an approximate question. Among the given options, none of them is close to 5.33, which may suggest a misprint in the options or a misunderstanding of the question. Nonetheless, if we have to choose the closest option, it is 'd' which is 7.