Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes. Find the probability of selecting a class that runs between 51.5 and 51.75 minutes. nothing ​(Round to three decimal places as​ needed.).

Answer 1

Answer: The probability that a given class period runs between 51.5 and 51.75 minutes = 0.025

The probability of selecting a class that runs between 51.5 and 51.75 minutes = 0.025

Step-by-step explanation:

The probability density function for random variable x uniformly distributed in [a,b] is given by:-

$f(x)=\dfrac{1}{b-a}$

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes. Find the probability that a given class

Let x be the lengths of her classes.

$f(x)=\dfrac{1}{56-46}=\dfrac{1}{10}=0.1$

Then, the probability that a given class period runs between 51.5 and 51.75 minutes will be :-

$P(51.5$

Hence, the probability that a given class period runs between 51.5 and 51.75 minutes = 0.025

The probability of selecting a class that runs between 51.5 and 51.75 minutes = 0.025