Question

Suppose that the time students wait for a bus can be described by a uniform random variable X, where X is between 5 minutes and 75 minutes. (a) What is the probability, P that a student will wait between 5 and 33 minutes for the next bus? P = (b) What is the probability, P that a student will have to wait at least 33 minutes for the next bus?

Answer 1

Answer:

a) 0.4

b) 0.6            

Step-by-step explanation:

We are given the following information in the question:

The time students wait for a bus can be described by a uniform random variable X, where X is between 5 minutes and 75 minutes.

a = 5, b = 75

Then,

$f(x) = \displaystyle\frac{1}{b-a} = \frac{1}{75-5} = \frac{1}{70}$

We are given a uniform distribution.

a) P(student will wait between 5 and 33 minutes)

P( 5 < x < 33)

$=\displaystyle\int_{33}^{5} f(x) dx\\\\=\displaystyle\int_{33}^{5} \frac{1}{70}dx\\\\=\frac{1}{70}[x]_{33}^{5} = \frac{1}{70}(33-5) = 0.4$

b) P(a student will have to wait at least 33 minutes)

P(33 < x < 75)

$=\displaystyle\int_{75}^{33} f(x) dx\\\\=\displaystyle\int_{75}^{33} \frac{1}{70}dx\\\\=\frac{1}{70}[x]_{75}^{33} = \frac{1}{70}(75-33) = 0.6$