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 50.75 and 51.25 minutes.

Answer 1

Answer: 0.05

Step-by-step explanation:

Given : Interval for uniform distribution : [46.0 minutes, 56.0 minutes]

The probability density function will be :-

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

The probability that a given class period runs between 50.75 and 51.25 minutes is given by :-

$P(50.75<x<51.25)=\int^{51.25}_{50.75}f(x)\ dx\\\\=(0.1)[x]^{51.25}_{50.75}\\\\=(0.1)(51.25-50.75)=0.05$

Hence, the probability that a given class period runs between 50.75 and 51.25 minutes = 0.05