Scores on the Scholastic Aptitude Test form a ND with a mean of 500 and SD of 100 what is the minimum score necessary to be in the top 15% of the SAT distribution?
Stuck on what to do on this question? Any answers?
To find the minimum score necessary to be in the top 15% of the SAT distribution, you'll need to use the inverse normal distribution (also known as the z-score). Here's how you can approach it:
1. Start by finding the z-score corresponding to the desired percentile. Since you want the top 15%, you need to find the z-score that corresponds to the area of 1 - 0.15 = 0.85.
2. Look up the z-score in a standard normal distribution table or use a z-score calculator. A z-score of 0.85 corresponds to approximately 1.036 in a standard normal distribution.
3. Now that you have the z-score, you can use the formula: z = (x - mean) / SD, where x is the score you want to find, mean is the mean of the distribution (500), and SD is the standard deviation (100).
4. Plug in the values and solve for x:
1.036 = (x - 500) / 100
5. Rearrange the equation to solve for x:
x - 500 = 1.036 * 100
x - 500 = 103.6
x = 103.6 + 500
x = 603.6
Therefore, the minimum score necessary to be in the top 15% of the SAT distribution is approximately 603.6.