Question

g A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 53.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes

Answer 1

Answer: 0.025

Explanation:

Given : A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between interval : [48.0 minutes, 53.0 minutes]

Let x be the lengths of her classes that are uniformly distributed between interval : [48.0 minutes, 53.0 minutes].

The probability density function for the given situation :-

`f(x)}=(1)/(55-45)=(1)/(10)`

The probability that a given class period runs between 51.25 and 51.5 minutes is given by :-

`P(51.25<x<51.5)=\int^(51.5)_(51.255)f(x)\ d(x)\\\\=(1)/(10)\int^(51.5)_(51.25)\ dx\\\\=(1)/(10)[x]^(51.5)_(51.25)\\\\=(1)/(10)(51.5-51.25)\\\\=(1)/(10)(0.25)\\\\=0.025`

Hence, the probability that a given class period runs between 51.25 and 51.5 minutes is 0.025 .