In the instructor's answer book for a mathematics text, 8% of the answers are incorrect. Use the Poisson approximation to express the probability that there are exactly 2
Incorrect answers for a homework set with 50 problems.
A) $\frac { e ^ { - \gamma } 8 ^ { 2 } } { 2 ! }$
B) $\frac { e ^ { - 8 } 2 ^ { 8 } } { 8 ! }$
C) $\frac { e ^ { - 4 } 2 ^ { 4 } } { 4 ! }$
D) $\frac { e ^ { - 4 } 4 ^ { 2 } } { 2 ! }$

Question

In the instructor's answer book for a mathematics text, 8% of the answers are incorrect. Use the Poisson approximation to express the probability that there are exactly 2
Incorrect answers for a homework set with 50 problems. 
A) $\frac { e ^ { - \gamma } 8 ^ { 2 } } { 2 ! }$
B) $\frac { e ^ { - 8 } 2 ^ { 8 } } { 8 ! }$
C) $\frac { e ^ { - 4 } 2 ^ { 4 } } { 4 ! }$
D) $\frac { e ^ { - 4 } 4 ^ { 2 } } { 2 ! }$

Quizplus · Accepted Answer

The Poisson approximation formula is $P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of successes (in this case, incorrect answers) and $k$ is the number of successes we're interested in. Here, with 8% of 50 problems being incorrect on average, $\lambda = 0.08 \times 50 = 4$. For exactly 2 incorrect answers, $k = 2$, so the correct formula is $\frac{e^{-4} 4^2}{2!}$.

In the Instructor's Answer Book for a Mathematics Text, 8 e−γ822!\frac { e ^ { - \gamma } 8 ^ { 2 } } { 2 ! }2!e−γ82​

In the Instructor's Answer Book for a Mathematics Text, 8 $\frac { e ^ { - \gamma } 8 ^ { 2 } } { 2 ! }$