Exam 9: Binomial Distribution

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If Q = 0.30 then P equals _________.

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The probability of 7 P events when N = 10 and P = 0.8 is the same as 3 Q events if Q = 0.2 and N = 10.

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The binomial distribution only applies to flipping coins and not to real life situations.

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If N = 18 the probability of obtaining a result as extreme or more extreme than 16 P events equals p (16) + p (17) + p (18).

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What is the probability of obtaining 2 or fewer heads if p ( H ) = 0.2 and 7 coins were tossed once?

(Short Answer)
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( P + Q )6 = P 6 +6 P 5 Q 5 +15 P 4 Q 2 + 20 P 3 Q 3 + 15 P 2 Q 4 + 6 P 5 Q 2 + Q 6. If P = 0.40, what is the exact probability of getting 3 P events? The answer to the previous question is found by evaluating which term in the expanded binomial expansion?

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Assuming the binomial distribution is appropriate, if N = 7, P = 0.40, and the number of P events = 2, the number of Q events = _________.

(Multiple Choice)
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List three commonly encountered situations where the binomial distribution is applicable and explain how the appropriate conditions are met in each.

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Table B in your textbook lists the binomial distribution for various N , P and Q values. According to the table, for N = 15, and P = Q = 0.50, p (15+'s) = 0.0000. Is p (15+'s) truly equal to zero? Explain.

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Assuming the binomial distribution is appropriate, if N = 6 and P = 0.50, the probability of getting exactly 5 P events = _________.

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The binomial expansion equals _________.

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For biased coins, the probability of getting 5 heads out of a toss of 5 coins equals the probability of getting 5 tails out of a toss of 5 coins.

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The binomial distribution applies equally well to discrete and continuous variables.

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One can appropriately apply the binomial distribution if P = 0.37 and Q = 0.63.

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If p ( H ) = 0.75 what is the probability that if 9 coins were tossed once that one would get 6 or more heads?

(Short Answer)
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A smaller N is required to use the normal approximation if P = 0.60 than if P = 0.80.

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What is the probability of tossing 6 unbiased coins once and getting 6 heads? What is the probability of getting 6 tails? What is the probability of obtaining either 6 heads or 6 tails?

(Essay)
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Suppose you flip 35 biased coins once. The probability of a head with each coin equals 0.30. What is the probability you will get 15 or more heads?

(Multiple Choice)
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The binomial distribution only applies to situations where P = 0.50.

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In one flip of 10 unbiased coins, what is the probability of getting 8 or more heads?

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