Question

Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimal places (when possible).
Required:
a. The mean of this distribution is :_________
b. The standard deviation is:________

Answer 1

Answer:

a) 27

b) 15

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 distribution is:

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

The variance of the uniform distribution is given by:

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

The standard deviation is the square root of the variance.

They can be said to follow a Uniform distribution from 1 to 53

This means that $a = 1, b = 53$

a. The mean of this distribution is

$M = \frac{a + b}{2} = \frac{1 + 53}{2} = 27$

b. The standard deviation is:

$s = \sqrt{V} = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(53-1)^{2}}{12}} = 15$