A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs between 50.25 and 50.5 minutes.
(50.5-50.25)/(52-50) = ?
.125
To find the probability that a given class period runs between 50.25 and 50.5 minutes, we need to calculate the probability of a random observation falling within this range in a uniform distribution.
In a uniform distribution, the probability density function (PDF) is constant within the range and zero outside it. Since the lengths of the classes are uniformly distributed between 50.0 and 52.0 minutes, the total range is 52.0 - 50.0 = 2.0 minutes.
The probability of a class running between 50.25 and 50.5 minutes is equal to the length of the interval (0.5 - 0.25 = 0.25) divided by the total range (2.0).
So, the probability is:
P(50.25 ≤ X ≤ 50.5) = (0.5 - 0.25) / 2.0 = 0.25 / 2.0 = 0.125
Therefore, the probability that a given class period runs between 50.25 and 50.5 minutes is 0.125 or 12.5%.