Question: Question 6
8.(d) Find the z score corresponding to a score of $X=45$ for when $\mu = 40$, and $\sigma = 2$
A. 2.50
B. 0.25
C. 0.40
D. 5
Question 7
#10. A score that is 6 points below the mean corresponds to a z-score of $z= -2.00$. What is the population standard deviation?
The population standard deviation is
D. 0.50
1. **State the problem:**
Find the z-score for a score $X=45$ given the mean $\mu=40$ and standard deviation $\sigma=2$.
2. **Formula:**
The z-score formula is:
$$z = \frac{X - \mu}{\sigma}$$
This formula tells us how many standard deviations a value $X$ is from the mean $\mu$.
3. **Substitute the values:**
$$z = \frac{45 - 40}{2}$$
4. **Calculate the numerator:**
$$z = \frac{5}{2}$$
5. **Simplify the fraction:**
$$z = \frac{\cancel{5}}{\cancel{2}} = 2.5$$
6. **Interpretation:**
The z-score corresponding to $X=45$ is $2.5$, meaning the score is 2.5 standard deviations above the mean.
**Final answer:**
**A. 2.50**