A statistics professor plans her classes so carefully that the lengths of her class are uniformly distributed between 46.0 and 56.0 minutes. Find the probablity that given class period runs less than 51.75 minutes
well, since 51.75 is 57.5% of the way between 46 and 56, ...
To find the probability that the class period runs less than 51.75 minutes, we can use the concept of a uniform distribution.
The uniform distribution means that all values within a given interval are equally likely. In this case, the intervals are between 46.0 and 56.0 minutes.
To find the probability, we can use the formula for the cumulative distribution function (CDF) of a uniform distribution:
P(X ≤ x) = (x - a) / (b - a)
Where:
- P(X ≤ x) is the probability that the random variable X is less than or equal to x
- x is the given value
- a is the lower limit of the interval
- b is the upper limit of the interval
In this case, x = 51.75, a = 46.0, and b = 56.0. Plugging these values into the formula, we get:
P(X ≤ 51.75) = (51.75 - 46.0) / (56.0 - 46.0)
Simplifying this expression, we have:
P(X ≤ 51.75) = 5.75 / 10
Hence, the probability that a given class period runs less than 51.75 minutes is 0.575 or 57.5%.