Respuesta :
The expected value is 50 then Carmen’s prediction is low because 200 times one-fourth is 50. Then the correct option is B.
How to calculate the expectation value?
Expectation can be taken as a weighted mean, weights being the probability of occurrence of that specific observation.
Thus, if the random variable is X, and its probability mass function is given as
[tex]E(X) = \sum_{i=1}^n( f(x_i) \times x_i)[/tex]
(n is the number of values X takes)
Carmen is going to roll an 8-sided die 200 times.
She predicts that she will roll a multiple of 4 twenty-five times.
The sample will be
Total event = 8 {1, 2, 3, 4, 5, 6, 7, 8}
Then the favorable event will be to roll an 8-sided die and get a multiple of 4. Then we have
Favorable event = 2 {4, 8}
Then the probability will be
[tex]\rm P = \dfrac{2}{8} = \dfrac{1}{4}[/tex]
A dice is rolled 200 times, then by the binomial theorem we have the expected value will be
[tex]E(x) = nP = 200 \times \dfrac{1}{4} = 50[/tex]
More about the expectation link is given below.
https://brainly.com/question/19585939
