The Normal distribution Quiz

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

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

2. $X\sim\mathrm{N}(40,2.5^2)$. Find the value of $Z$ when $X=35$.

• A. $-2$
• B. $2$
• C. $-5$
• D. $-0.8$

3. Find $\mathrm{P}(Z<-1.2)$, given $\Phi(1.2)=0.8849$.

• A. $0.8849$
• B. $0.3849$
• C. $0.1151$
• D. $0.2302$

4. Which value of $z$ has $\mathrm{P}(Z<z)=0.975$?

• A. $0.975$
• B. $1.645$
• C. $2.326$
• D. $1.960$

5. $X\sim\mathrm{N}(\mu,\sigma^2)$ with $\mathrm{P}(X<30)=0.5$ and $\mathrm{P}(X<36)=0.9332$. Find $\sigma$.

• A. $6$
• B. $9$
• C. $4$
• D. $16$