WE have 10 questions, the answer is either right or wrong whatever the number of choices. Then P(right) = 1/2 and Q(wrong) =1/2 Moreover as per the given of the problem, he may get at least 7 right answers, that means he can get 7 OR 8 OR 9 OR 10 right answers: Here-below the binomial probability distribution:
a) for 7 exactly right answers : ¹⁰C₇ (1/2)⁷(1/2)³ = 0.117187
b) for 8 exactly right answers : ¹⁰C₈ (1/2)⁸(1/2)² = 0.043945
c) for 9 exactly right answers : ¹⁰C₉ (1/2)⁹(1/2)¹ = 0.009656
d) for 10 exactly right answers : ¹⁰C₁₀ (1/2)¹⁰(1/2)⁰ = 0.000488 ------------- Σ (PROBABILITY) = 0.171276
Hello! To find the answer to this, we must add all of the first 5 numbers. When you do that, the sum should be 81. You must do 16 * 6 to find the number of points combined he needs to add up to the average. 16 * 6 = 96. 96 - 81 = 15. On the 6th test, you must score 15 points to have an average of 16 points. The answer is 15.
