Question

In a normal distribution with mean of 150 and standard deviation of 30. What percentage of scores are more than 3 standard deviations from the mean? a) 0.13%

b) 0.27%
c) 0.55%
d) 0.72%

Answer 1

Approximately 0.3% of scores are more than 3 standard deviations from the mean.

Step-by-step explanation:

The percentage of scores that are more than 3 standard deviations from the mean can be found using the empirical rule for normal distributions. The empirical rule states that approximately 99.7% of the scores lie within 3 standard deviations of the mean, leaving only 0.3% of scores beyond this range. Since we are looking for the percentage beyond this range, we can subtract 99.7% from 100% to find that approximately 0.3% of scores are more than 3 standard deviations from the mean. This method illustrates the small fraction of values lying outside the three standard deviation range.