Question

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700?

a) Approximately 15.87%
b) Approximately 34.13%
c) Approximately 34.13%
d) Approximately 15.87%

Answer 1

The probability of scoring between 600 and 700 on a standardized test is approximately 13.59%.

Step-by-step explanation:

To find the probability of a score between 600 and 700 on a standardized test, we need to calculate the z-scores for each score and use the z-table to find the corresponding probabilities. The formula for calculating the z-score is:

z = (score - mean) / standard deviation

For a score of 600, the z-score would be (600 - 500) / 100 = 1. The corresponding probability for a z-score of 1 is approximately 0.8413.

For a score of 700, the z-score would be (700 - 500) / 100 = 2. The corresponding probability for a z-score of 2 is approximately 0.9772.

To find the probability of a score between 600 and 700, we subtract the probability of a score less than 600 from the probability of a score less than 700:

P(600 < x < 700) = P(x < 700) - P(x < 600) = 0.9772 - 0.8413 = 0.1359.