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

a) 27

b) 15

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 = (a + b)/(2)`

The variance of the uniform distribution is given by:

`V = ((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 = (a + b)/(2) = (1 + 53)/(2) = 27`

b. The standard deviation is:

`s = √(V) = \sqrt{((b-a)^(2))/(12)} = \sqrt{((53-1)^(2))/(12)} = 15`