4.12 Standardisation and inverse normal with unknown parameters Quiz

1. $X\sim N(20,9)$. Find the $z$-value of $x=26$.

• A. $2$
• B. $\frac{2}{3}$
• C. $6$
• D. $-2$

2. $X\sim N(100,15^{2})$. Which value has $z=-1.2$?

• A. $118$
• B. $82$
• C. $98.8$
• D. $101.2$

3. $X\sim N(\mu,5^{2})$ and $P(X<30)=0.25$. Find $\mu$, correct to 3 significant figures.

• A. $26.6$
• B. $33.4$
• C. $30.7$
• D. $29.3$

4. $X\sim N(40,\sigma^{2})$ and $P(X>46)=0.05$. Find $\sigma$, correct to 3 significant figures.

• A. $3.65$
• B. $9.87$
• C. $4.68$
• D. $3.08$

5. For $X\sim N(\mu,\sigma^{2})$, $P(X<a)=0.3$. Which statement is true?

• A. $a>\mu$
• B. $a<\mu$
• C. $a=\mu$
• D. It depends on $\sigma$