Question

Suppose two people go on a trivia game night adventure. One of them answers questions correctly .45 of the time. That person is asked 64 questions over the span of the night, and the number he gets wrong is random var X.

1) What is probability that he gets at least 20 but less than 33 questions correct

2)He gets $4 per question correct, and loses $2 per wrong. What is the expected value of the winnings with a $50 entrance fee

Answer 1

1)

Here

Using Normal approximation to Binomial distribution,

Required probability =

{Due to continuity correction as a result of using Normal approximation for Binomial distribution}

2)

Now,

So, he expects 35.2 wrong answers and 64-35.2=28.8 correct answers.

Expected value of winnings = 4(28.8)-2(35.2)-50 = -5.2

i.e. a loss of $5.2