Answer:
Carmen's prediction is low because 200 times
is 50.
Step-by-step explanation:
First of all we are going to define the sample space for this exercise.
The sample space is Ω = {1,2,3,4,5,6,7,8}
Given the event A : ''Roll an 8-sided die an get a multiple of 4''
The probability for the event A is ![P(A)=\frac{2}{8}=\frac{1}{4}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B2%7D%7B8%7D%3D%5Cfrac%7B1%7D%7B4%7D)
Because they are two numbers (4 and 8) over a total of eight numbers (1,2,3,4,5,6,7,8) that are multiple of 4.
Now, given the random variable X : ''Total of numbers multiples of 4 If she rolls
an 8-sided die 200 times''
X can be modeled as a Binomial random variable.
X ~ Bi (n,p)
X ~ Bi (200,
)
In which n is the total times she rolls the 8-sided die and p is the success probability.We define a success as obtain a number multiple of 4.
The mean for this variable is
![E(X)=np=200.\frac{1}{4}=50](https://tex.z-dn.net/?f=E%28X%29%3Dnp%3D200.%5Cfrac%7B1%7D%7B4%7D%3D50)
We answer that Carmen's prediction is low because 200 times
is 50.