The ages of middle-managers in an organisation is uniformly distributed and ranges from 41 to 47 years.

What is the probability that a middle-manager is from 35 to 40 years old?

Question

The ages of middle-managers in an organisation is uniformly distributed and ranges from 41 to 47 years.

What is the probability that a middle-manager is from 35 to 40 years old?

BlackTom AI · Accepted Answer

The problem states that the ages of middle-managers are uniformly distributed and lie between 41 and 47 years. This means the support (possible values) of the distribution is the interval [41, 47].

Consider the target age range 35 to 40 years. This interval lies entirely below the lower bound of the distribution’s support (41). For a continuous uniform distribution, the probability of falling in any interval outside the supported range is zero because there are no possible values in that outside region.

A quick way to formalize this is to use the overlap approach: the overlapping length between [35, 40] and [41, 47] is max(0, min(40, 47) - max(35, 41)) = max(0, 40 - 41) = 0. Dividing by the total length of the support (47 - 41 = 6) would give 0/6 = 0. But since there is no overlap at all, the probability is simply 0.

Therefore, the probability that a randomly selected middle-manager aged uniformly from 41 to 47 falls within the 35–40 range is 0.

BSTA011 Week 5 practice quiz

The ages of middle-managers in an organisation is uniformly distributed and ranges from 41 to 47 years. What is the probability that a middle-manager is from 35 to 40 years old?

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