Refer to the following normal curve to answer the questions below What percentage of the scores were between 60 and 75 points?      percent

To calculate the percentage of scores between 60 and 75 points on a normal curve, we typically need the mean (μ) and standard deviation (σ) of the distribution; however, since these values are not provided in your question, I will assume some common values for demonstration purposes.

Let's go through the process assuming a mean of 70 and a standard deviation of 10.

1. ### Break Down the Problem

1. Identify the values of interest: 60 and 75.
2. Determine the corresponding Z-scores for these values using the mean and standard deviation.
3. Use the Z-scores to find the area under the normal curve.

2. ### Relevant Concepts

The Z-score is calculated using the formula: $Z = \frac{X - \mu}{\sigma}$ where $X$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

3. ### Analysis and Detail

1. Calculate the Z-score for 60 points: $Z_{60} = \frac{60 - 70}{10} = \frac{-10}{10} = -1$

2. Calculate the Z-score for 75 points: $Z_{75} = \frac{75 - 70}{10} = \frac{5}{10} = 0.5$

3. Now, we look up the Z-scores in a standard normal distribution table or use a calculator:

   • The area to the left of $Z = -1$ is approximately 0.1587 (15.87%).
   • The area to the left of $Z = 0.5$ is approximately 0.6915 (69.15%).

4. To find the percentage of scores between 60 and 75, subtract the area at $Z = -1$ from the area at $Z = 0.5$: $\text{Percentage} = \text{Area at } Z_{75} - \text{Area at } Z_{60} = 0.6915 - 0.1587 = 0.5328$

4. ### Verify and Summarize

Converting the decimal to a percentage: $0.5328 \times 100 \approx 53.28\%$

Final Answer

The percentage of scores between 60 and 75 points is approximately 53.28%.