Respuesta :
Answer:
The approximate probability that more than six students were born on Christmas day is P=0.105.
Step-by-step explanation:
This can be modeled as a binomial variable, with n=1460 and p=1/365.
The sample size n is the total amount of students and the probability of success p is the probability of each individual of being born on Christmas day.
As the sample size is too large to compute it as a binomial random variable, we approximate it to the normal distribution with the following parameters:
[tex]\mu=n\cdot p=1460\cdot (1/365)=4\\\\\sigma=\sqrt{n\cdot p(1-p)}=\sqrt{1460\cdot(1/365)\cdot(364/365)}=\sqrt{3.989}=1.997[/tex]
We want to calculate the probability that more than 6 students were born on Christmas day. Ww apply the continuity factor and we write the probability as:
[tex]P(X>6.5)[/tex]
We calculate the z-score for X=6.5 and then calculate the probability:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{6.5-4}{1.997}=\dfrac{2.5}{1.997}=1.252\\\\\\P(X>6.5)=P(z>1.252)=0.105[/tex]
