1. What score has a percentile rank of \( 60 \% \) ? ( 2 pts) 2. What score has a percentile rank of \( 50 \% \) ( 2 pts) 3. What is the percentile rank for \( X=45 \) ? ( 2 pts) 4. What is the percentile rank for \( X=32 \) ? ( 2 pts)

To accurately answer these questions about percentile ranks and scores, additional information about the data distribution is required. Specifically, details such as the mean, standard deviation, or the actual dataset are necessary to determine the exact scores or percentile ranks. However, I can provide a general explanation of how to approach these types of problems: 1. **Finding a Score Given a Percentile Rank (Questions 1 & 2):** - **Percentile Rank:** Indicates the percentage of scores in a distribution that a particular score is above. - **Approach:** If the distribution is normal, you can use the z-score corresponding to the desired percentile and then convert it to the actual score using the formula: \[ \text{Score} = \mu + (z \times \sigma) \] where \( \mu \) is the mean and \( \sigma \) is the standard deviation. 2. **Finding the Percentile Rank for a Given Score (Questions 3 & 4):** - **Approach:** Determine where the score falls within the distribution. For a normal distribution, you can find the z-score and then use the standard normal distribution table to find the corresponding percentile rank. \[ z = \frac{X - \mu}{\sigma} \] Then, use the z-score to find the percentile. **Example Using a Normal Distribution:** Assume a normal distribution with a mean (\( \mu \)) of 50 and a standard deviation (\( \sigma \)) of 10. 1. **What score has a percentile rank of 60%?** - Find the z-score for the 60th percentile (approximately 0.253). - Calculate the score: \[ \text{Score} = 50 + (0.253 \times 10) = 52.53 \] 2. **What score has a percentile rank of 50%?** - The 50th percentile corresponds to the median, which in a normal distribution is the mean. - **Score:** 50 3. **What is the percentile rank for \( X = 45 \)?** - Calculate the z-score: \[ z = \frac{45 - 50}{10} = -0.5 \] - The percentile rank for \( z = -0.5 \) is approximately 30.85%. 4. **What is the percentile rank for \( X = 32 \)?** - Calculate the z-score: \[ z = \frac{32 - 50}{10} = -1.8 \] - The percentile rank for \( z = -1.8 \) is approximately 3.58%. **Note:** These calculations are based on the assumed normal distribution parameters. For precise answers, please provide the specific data or distribution details.