Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.046.0 and 56.056.0 minutes. Find the probability that a given class period runs between 50.2550.25 and 51.2551.25 minutes. Find the probability of selecting a class that runs between 50.2550.25 and 51.2551.25 minutes.

Answer 1

The probability of selecting a class that runs between 50.2550.25 and 51.2551.25 minutes is 0.10

Explanation:

The Uniform Distribution, also known as Rectangular Distribution, is a type of Continuous Probability Distribution. It has a continuous random variable restricted to a finite interval and its probability function has a constant density during this interval.

The formula of probability if given by:

f(x)=

`\left \{ {{(1)/(b-a); \ a \leq x \leq b  } \atop {0}; \ x \ otherwise } \right.`

In this exercise a= 46.0 and b= 56.0

The probability of selecting a class that runs between 50.2550.25 and 51.2551.25 minutes is:

`\int\limits^(51.25)_(50.25) {(1)/(56-46) } \, dx = \int\limits^(51.25)_(50.25) {(1)/(10) } \, dx = (1)/(10) * (51.25 - 50.25)=(1)/(10)=0.1`