1) Suppose a quiz has 9 multiple choice questions. Each question has 5 answer ch
ID: 3042649 • Letter: 1
Question
1) Suppose a quiz has 9 multiple choice questions. Each question has 5 answer choices. If a student takes the quiz and randomly guesses on every question....
A) Find the probability the student gets between 3 and 8, exclusive, questions correct.
B) Find the probability the student gets more than 5 questions correct.
2) One state lottery has 900 prizes of $1; 105 prizes of $10; 20 prizes of $70; 5 prizes of $355; 2 prizes of $1130; and 1 prize of $2400. Assume that 22000 lottery tickets are issued and sold for $1.
A) What is the lottery's expected profit per ticket?
B) What is the lottery's standard deviation of profit per ticket?
(Make sure you carry all decimals until you reach your answer, then round to four decimals)
Explanation / Answer
1)
We use binomial distribution here
n=9
p=1/5 =0.2
q=1-p=1-0.2 =0.8
P=nCr p^r q^(n-r)
A) We need to find P(3<r<8) =P(r=4) +P(r=5) +P(r=6) +P(r=7)
=9C4 0.2^4 0.8^(9-4) + 9C5 0.2^5 0.8^(9-5) + 9C6 0.2^6 0.8^(9-6) + 9C7 0.2^7 0.8^(9-7)
=9C4 0.2^4 0.8^(5) + 9C5 0.2^5 0.8^(4) + 9C6 0.2^6 0.8^(3) + 9C7 0.2^7 0.8^(2)
=0.06606 + 0.016515 + 0.0027525 + 0.0002949
=0.0856
B) P(more than 5 correct) = P(r=6) +P( r=7) +P(r=8) + P(r=9)
=9C6 0.2^6 0.8^(9-6) + 9C7 0.2^7 0.8^(9-7) + 9C8 0.2^8 0.8^(9-8) + 9C9 0.2^9 0.8^(9-9)
=9C6 0.2^6 0.8^(3) + 9C7 0.2^7 0.8^(2) + 9C8 0.2^8 0.8^(1) + 9C9 0.2^9 0.8^(0)
=0.0027525 + 0.0002949 + 0.000018432 + 0.000000512
=0.0031
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