The normal distribution Quiz

1. $X\sim N(50,4^2)$. Find $P(X>54)$.

• A. $0.841$
• B. $0.159$
• C. $0.023$
• D. $0.341$

2. Compared with $N(10,2^2)$, the curve for $N(10,5^2)$ is...

• A. wider and flatter, with the same centre
• B. narrower and taller, with the same centre
• C. the same shape, shifted to the right
• D. wider, with its peak at 25

3. For $X\sim N(20,25)$, where are the points of inflection?

• A. $x=-5$ and $x=45$
• B. $x=0$ and $x=40$
• C. $x=18$ and $x=22$
• D. $x=15$ and $x=25$

4. $P(X<\mu-2\sigma)=0.0228$. What is $P(X>\mu+2\sigma)$?

• A. $0.9772$
• B. $0.0456$
• C. $0.0228$
• D. $0.5$

5. $X\sim N(100,10^2)$ and $P(X<x)=0.975$. Find $x$.

• A. $110$
• B. $119.6$
• C. $101.96$
• D. $196$