Answer:
[tex] P(X>30) = 1-P(X<30) = 1- \frac{30-1}{53-1}= 1- 0.56 = 0.44[/tex]
Step-by-step 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:
[tex] X \sim Unif (a= 1, b =53)[/tex]
And for this case we want this probability:
[tex] P(X>30)[/tex]
And for this case we can use the cumulative distribution function of the uniform ditribution given by:
[tex] F(x) = \frac{x-a}{b-a}, a\leq X \leq b[/tex]
And using this formula and the complement rule we have this:
[tex] P(X>30) = 1-P(X<30) = 1- \frac{30-1}{53-1}= 1- 0.56 = 0.44[/tex]
