Question

The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random variable ranging from 2 to 7. Find the mean and standard deviation of this random variable. (Round your answers to 2 decimal places.) Mean Standard deviation

Answer 1

Answer:

The mean is 4.5 and the standard deviation is 1.44.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform probability distribution is:

$M = \frac{(a + b)}{2}$

The standard deviation of the uniform probability distribution is:

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

Uniformly distributed random variable ranging from 2 to 7.

This means that $a = 2, b = 7$.

So

$M = \frac{(2 + 7)}{2} = 4.5$

$S = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(7 - 2)^{2}}{12}} = 1.44$

The mean is 4.5 and the standard deviation is 1.44.