Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 58.0 minutes. Find the probability that a given class period runs between 50.25 and 50.5 minutes. Find the probability of selecting a class that runs between 50.25 and 50.5 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 the interval [48.0 minutes, 58.0 minutes].

The probability density function :-

`f(x)=(1)/(58-48)=(1)/(10)`

Now, the probability that a given class period runs between 50.25 and 50.5 minutes is given by :-

`\int^(50.5)_(50.25)\ f(x)\ dx\\\\=\int^(50.5)_(50.25)\ (1)/(10)\ dx\\\\=(1)/(10)|x|^(50.5)_(50.25)\\\\=(1)/(10)\ [50.5-50.25]=(1)/(10)*(0.25)=0.025`

Hence, the probability that a given class period runs between 50.25 and 50.5 minutes =0.025

Similarly , the probability of selecting a class that runs between 50.25 and 50.5 minutes = 0.025