A multiple-choice standard test contains total of 25 questions, each with four answers. Assume that a student just guesses on each question and all questions are answered independently. (a) What is the probability that the student answers more than 20 questions correctly

Step-by-step explanation:

If we call x the number of correct answers, we can said that P(x) follows a Binomial distribution, because we have 25 questions that are identical and independent events with a probability of 1/4 to success and a probability of 3/4 to fail.

So, the probability can be calculated as:

Where n is 25 questions, p is the probability to success or 0.25 and q is the probability to fail or 0.75.

Additionally,

So, the probability that the student answers more than 20 questions correctly is equal to:

Where, for example, P(21) is equal to:

Finally, P(x>20) is equal to:

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363