Respuesta :
Answer:
Option b) 0.161
Step-by-step explanation:
We are given the following information:
We treat correct as a success.
P(Correct Answer) = [tex]\frac{1}{5}[/tex] = 0.2
Then the number of questions follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 11
We have to evaluate:
P(answer at least 4 questions correctly)
[tex]P(x \geq 4)\\=1 - P(x = 0) - P(x = 1) - P(x = 2) - P(x = 3)\\=1 - \binom{11}{0}(0.2)^0(1-0.2)^{11} - ... - \binom{11}{3}(0.2)^3(1-0.2)^{8}\\=1 -0.085 -0.237-0.296 - 0.221\\= 0.161[/tex]
Thus, 0.161 is the probability that Richard will answer at least 4 questions correctly.
Option b) 0.161
