Answer:
The probability of getting x correct answers is given by[tex]P(X = x) = (8Cx)(0.65^{x})(0.35^{8-x})[/tex] and P(X < 4) = 0.1061
Step-by-step explanation:
We have [tex]n=8[/tex] trials, each with probability of success given by [tex]p=0.65[/tex]. Let X be the random variable that represents the number of correct answers gotten by random guesses, then, X has a binomial distribution, and so, [tex]P(X = x) = (8Cx)(0.65^{x})(0.35^{8-x})[/tex], and [tex]P(X < 4)=\sum_{x=0}^{3}(8Cx)(0.65^{x})(0.35^{8-x})=0.1061[/tex], this is the probability that the number x of correct answers is fewer than 4.
