Find the z-score of a person who scored 225 on the exam with mean 200 and standard...

1. Identify the given values: We are given a normal distribution with a mean ($\mu$) of $200$ and a standard deviation ($\sigma$) of $50$. We want to find the z-score for a specific score ($x$) of $225$.

2. State the z-score formula: The z-score formula is used to determine how many standard deviations a value is from the mean. It is defined as:
$$z = \frac{x - \mu}{\sigma}$$

3. Substitute the values into the formula: Plug in $x = 225$, $\mu = 200$, and $\sigma = 50$ into the equation:
$$z = \frac{225 - 200}{50}$$

4. Perform the calculation: First, subtract the mean from the score:
$$225 - 200 = 25$$
Next, divide the result by the standard deviation:
$$z = \frac{25}{50} = 0.5$$

1. Conclusion: The z-score for a person who scored $225$ is $0.5$.