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 50.7550.75 and 51.7551.75 minutes.

Answer 1

Answer: 0.1

Explanation:

Let x be a random variable that is uniformly distributed on interval [a,b]

The probability density function for x :-

`f(x)=(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.

Let x be the random variable that denotes the lengths of her classes.

The probability density function =
`f(x)=(1)/(56-46)=(1)/(10)`

Now, the probability that a given class period runs between 50.75 and 51.75 minutes will be :-

`P(50.75<x<51.75)=\int^(51.75)_(50.75)\ f(x)\ dx\\\\=\int^(51.75)_(50.75)\ (1)/(10)\ dx\\\\=(1)/(10)[x]^(51.75)_(50.75)\\\\=(1)/(10)[51.75-50.75]=(1)/(10)(1)=0.1`

Hence, the required probability = 0.1