Question

The duration of a professor's class has continuous uniform distribution between 49.2 minutes and 55.5 minutes. If one class is randomly selected and the probability that the duration of the class is longer than a certain number of minutes is 0.468, then find the duration of the randomly selected class, i.e., if P ( x > c )

Answer 1

Answer:

The duration of the randomly selected class is 52.6 minutes.

Step-by-step explanation:

The random variable X is defined as the duration of a professor's class.

It is provided that, $X\sim Unif(49.2, 55.5)$.

The pdf of X is:

$f_{X}(x)=\frac{1}{55.5-49.2};\ 49.2$

It is provided that the probability that the duration of the class is longer than c number of minutes is 0.468.

That is, P (X > c) = 0.468.

Compute the value of c as follows:

$P(X>c)=0.468\\\\\int\limits^{55.5}_{c}{\frac{1}{55.5-49.2}}=0.468\\\\\frac{1}{6.3}\times [x]^{55.5}_{c}=0.468\\\\55.5-c=2.9484\\\\x=52.5516\\\\x\approx 52.6$

Thus, the duration of the randomly selected class is 52.6 minutes.