Question

The distribution of scores on a standardized aptitude test is approximately normal with a mean of 490 and a standard deviation of 105. What is the minimum score needed to be in the top 5% 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 5% on this standardized aptitude test is 650.

Step-by-step explanation:

To find the minimum score needed to be in the top 5% on this test, we need to find the z-score that corresponds to the top 5% of the normal distribution. The z-score can be calculated using the formula:

z = (x - mean) / standard deviation

Substituting the given values, we have:

z = (x - 490) / 105

To find the minimum score, we need to find the x value that corresponds to a z-score of 1.645 (which represents the top 5%). Rearranging the equation, we have:

x = z * standard deviation + mean

Substituting the values, we get:

x = 1.645 * 105 + 490

Calculating this gives us approximately 649.725. Rounding this to the nearest integer, the minimum score needed to be in the top 5% on this test is 650.