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:

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

Step-by-step 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:

$f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b$

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

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

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

Answer 2

Answer: 0.050

I just did it and i got it right.