Question

Assume that random guesses are made for eight multiple choice questions on an SAT​ test, so that there are nequals8 ​trials, each with probability of success​ (correct) given by pequals0.65. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.

Answer 1

Answer:

The probability of getting x correct answers is given by$P(X = x) = (8Cx)(0.65^{x})(0.35^{8-x})$ and P(X < 4) = 0.1061

Step-by-step explanation:

We have $n=8$ trials, each with probability of success given by $p=0.65$. 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, $P(X = x) = (8Cx)(0.65^{x})(0.35^{8-x})$, and $P(X < 4)=\sum_{x=0}^{3}(8Cx)(0.65^{x})(0.35^{8-x})=0.1061$, this is the probability that the number x of correct answers is fewer than 4.