The Normal distribution Quiz

1. $X\sim N(10,4)$. What is the standard deviation of $X$?

• A. $4$
• B. $2$
• C. $16$
• D. $10$

2. $X\sim N(50,10^2)$. Find $P(X<40)$.

• A. $0.8413$
• B. $0.3413$
• C. $0.1587$
• D. $0.0228$

3. The points of inflection of the Normal curve for $N(20,3^2)$ are at

• A. $x=17$ and $x=23$
• B. $x=11$ and $x=29$
• C. $x=14$ and $x=26$
• D. $x=20$ only

4. $P(Z<z)=0.95$ gives $z=1.645$. For $X\sim N(50,10^2)$, the value $x$ with $P(X<x)=0.95$ is

• A. $51.6$
• B. $16.45$
• C. $66.5$
• D. $33.6$

5. $X\sim B(200,0.5)$ is approximated by $Y\sim N(\mu,\sigma^2)$. What are $\mu$ and $\sigma^2$?

• A. $100$ and $50$
• B. $100$ and $100$
• C. $200$ and $50$
• D. $100$ and $7.07$