Question

Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform Distribution from 1 – 53 (spread of 52 weeks). Round all answers to two decimal places. Find the probability that a person will be born after week 30 is "P(x > 30)" = ?

Answer 1

`P(X>30) = 1-P(X<30) = 1- (30-1)/(53-1)= 1- 0.56 = 0.44`

Explanation:

For this case we can define the random variable X as "births of a population", and for this case we know that the distribution of X is given by:

`X \sim Unif (a= 1, b =53)`

And for this case we want this probability:

`P(X>30)`

And for this case we can use the cumulative distribution function of the uniform ditribution given by:

`F(x) = (x-a)/(b-a), a\leq X \leq b`

And using this formula and the complement rule we have this:

`P(X>30) = 1-P(X<30) = 1- (30-1)/(53-1)= 1- 0.56 = 0.44`