Assume that random guesses are made for ninenine multiple choice questions on an SAT test, so that there are nequals=99 trials, each with probability of success (correct) given by pequals=0.50.5. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 44.

The probability that the number of correct answers is 4 is 0.2461.

Step-by-step explanation:

Let X = number of correct answers.

The probability that an answer is correct is,P (X) = p = 0.50.

The total number of questions is, n = 9.

The event of an answer being correct is independent of the other answers.

The success of each trial is defined as a correct answer with equal probability of success for each trial, i.e. 0.50.

The random variable X follows a Binomial distribution with parameter n = 9 and p = 0.50.

The probability mass function of X is:

Compute the value of P (X = 4) as follows:

Thus, the probability that the number of correct answers is 4 is 0.2461.

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