Question

The distribution of scores on a standardized aptitude test is approximately normal with a mean of 520 and a standard deviation of 100 . What is the minimum score needed to be in the top 15% on this test?

Carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer.

Answer 1

The minimum score needed to be in the top 15% on this test is 416.

Step-by-step explanation:

To find the minimum score needed to be in the top 15% on this test, we need to find the z-score corresponding to the 15th percentile, as the z-score represents the number of standard deviations above or below the mean a given score is.

Using the standard normal distribution table, we find that the z-score for the 15th percentile is approximately -1.04.

To find the corresponding score, we can use the formula z = (x - mean) / standard deviation and solve for x. Rearranging the formula, we have x = z * standard deviation + mean.

Plugging in the values, we get x = -1.04 * 100 + 520 = 416.

Therefore, the minimum score needed to be in the top 15% is 416, rounded to the nearest integer.