Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. Find the probability that a given class period runs between 50.75 and 51.25 minutes. Find the probability of selecting a class that runs between 50.75 and 51.25 minutes.

Answer 1

Answer: 0.050

I just did it and i got it right.

Answer 2

The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.

Explanation:

Let the random variable X represent the lengths of the classes.

The random variable X is uniformly distributed within the interval 49.0 and 54.0 minutes.

The probability density function of X is:

`f_(X)(x)=(1)/(b-a);\ a<X<b,\ a<b`

Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:

`P(50.75<X<51.25)=\int\limits^(51.25)_(50.75){(1)/(54-49)}\, dx\\\\=(1)/(5)* [x]^(51.25)_(50.75)\\\\=(51.25-50.75)/(5)\\\\=0.10`

Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.