Question

On the math portion of the sat, the scores are roughly normally distributed with mean 500 and standard deviation 100. what percentage of sat scores are above 400?

Answer 1

The percentage of SAT scores above 400 is approximately 84.13%.

Step-by-step explanation:

The SAT scores on the math portion are roughly normally distributed with a mean of 500 and a standard deviation of 100. To find the percentage of SAT scores above 400, we need to determine the proportion of scores that are greater than 400. Since the distribution is normal, we can use the standardized normal distribution table to calculate the proportion.

First, we calculate the z-score for a score of 400 using the formula:

z = (X - mean) / standard deviation = (400 - 500) / 100 = -1

The z-score of -1 corresponds to an area of 0.1587 on the standardized normal distribution table. To find the percentage of scores above 400, we subtract this proportion from 1:

Percentage above 400 = 1 - 0.1587 = 0.8413 or 84.13%