If the random variable X is uniformly distributed between 40 and 60, then P(35 ≤ X ≤ 45) is:

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BlackTom AI · Accepted Answer

We start by identifying the distribution and the interval of interest. The random variable X is uniformly distributed on [40, 60], meaning it has equal probability density across this interval and the total length of the support is 60 − 40 = 20.

To find P(35 ≤ X ≤ 45), we look at the portion of the interval [40, 60] that lies within [35, 45]. The intersection of these two intervals is [40, 45], which has length 45 − 40 = 5.

For a continuous uniform distribution, probability is proportional to the length of the interval of interest relative to the total length of the support. Therefore, P(35 ≤ X ≤ 45) = length of intersection / total length = 5 / 20 = 0.25.

If the provided multiple-choice options include a value of 0.25 (for example, labeled as c. 0.25), that option would reflect this computed probability. However, since the answer options are not provided in the prompt, this calculation yields the numerical result for the specified probability regardless of option labeling.

COMM111_S2 Quiz 4: Continuous Distributions

If the random variable X is uniformly distributed between 40 and 60, then P(35 ≤ X ≤ 45) is:

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