Question

Question 7 (4 points) A student takes a multiple choice test consisting of 5 questions where there are 4 choices per question. Also, each question is worth 20 points. Suppose the student guesses on each question. Let X be the number of questions the student gets correct. The probability distribution for X is given below. Find the probability that the student gets at least a 60 on the test. Give your answer to four decimal places. x10 11 12 13 14 15 P(X=x) 0.2373 0.3955 0.2637 0.0879 0.0146.0010 Your Answer: Answer

Answer 1

Solution:

Here, we have to find the probability that the student gets at least a 60 on the test.

Each question is worth 20 points.

Three questions are worth 60 points.

So, we have to find P(X≥3)

P(X≥3) = P(X=3) + P(X=4) + P(X=5)

From given probability distribution, we have

P(X=3) = 0.0879

P(X=4) = 0.0146

P(X=5) = 0.0010

P(X≥3) = P(X=3) + P(X=4) + P(X=5)

P(X≥3) = 0.0879 + 0.0146 + 0.0010

P(X≥3) = 0.1035

Answer: 0.1035