Poisson approximation to the binomial Quiz

1. $X\sim B(150,0.02)$. Which Poisson distribution approximates $X$?

• A. $\text{Po}(150)$
• B. $\text{Po}(3)$
• C. $\text{Po}(0.02)$
• D. $\text{Po}(7500)$

2. Which binomial distribution is best approximated by a Poisson distribution?

• A. $B(10,0.5)$
• B. $B(20,0.4)$
• C. $B(100,0.5)$
• D. $B(100,0.03)$

3. $X\sim B(200,0.01)$. Use a Poisson approximation to find $P(X=1)$.

• A. $0.271$
• B. $0.135$
• C. $0.406$
• D. $0.020$

4. For $X\sim B(n,p)$ with $p$ small, which value is close to $\text{Var}(X)$?

• A. $p$
• B. $n$
• C. $np$
• D. $p(1-p)$

5. $X\sim B(300,0.01)$. Use a Poisson approximation to find $P(X\ge2)$.

• A. $0.199$
• B. $0.801$
• C. $0.423$
• D. $0.577$