Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the student will get 8 or fewer answers correct? A. Find the probability that X=8 in a binomial distribution with n = 20 and p=0.5. B. Find the area between 0 and 8 in a uniform distribution that goes from 0 to 20. C. Find the probability that X=8 for a normal distribution with mean of 10 and standard deviation of D. Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

To obtain the probability that a student gets 8 or fewer answers correct, we find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

Recall :

Using a binomial probability calculator :

Hence, the Cummulative probability is the probability for 8 is the total sum of the probabilities of x = 8 or less in the experiment.

Therefore, the appropriate option is D.

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D. Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. The probability of the student is guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

20 questions

This means that

How would you find the probability that the student will get 8 or fewer answers correct?

That is, it is the same as the cumulative probability for 8.

So the correct answer is:

D. Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

step-by-step explanation: