Respuesta :
Answer:
a) We expect to have 135 people to have had chickenpox in their childhood.
b) No, I would not be surprised, as the probability is not low.
z = -0.6812
c) P(X≤132)=0.248
Step-by-step explanation:
a) This is a binomial random variable, with n=150 and p=0.9, so we can calculate the expected value as:
[tex]E(X)=np=150\cdot 0.9=135[/tex]
b) To answer this we can calculate the probability that 132 people or fewer have had chickenpox in their childhood.
This binomial random variable can be approximated by a normal distribution, with the following parameters:
[tex]\mu=np=150\cdot 0.9=135\\\\\sigma=\sqrt{np(1-p)}=\sqrt{150\cdot 0.9\cdot 0.1}=\sqrt{13.5}=3.67[/tex]
To calculate the probability that 132 people or fewer have had chickenpox in their childhood we compute the z-score for X=132.5 (as we apply the continuity factor) and calculate the probability using the standard normal distribution:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{132.5-135}{3.67}=\dfrac{-2.5}{3.67}=-0.6812\\\\\\P(X<132.5)=P(z<-0.6812)=0.248[/tex]
