Some IQ scores are standardized with a mean of 100 and a standard deviation of 16. Using the 68-95-99.7 Rule, Determine: What percent of people would have an IQ score 68 and 84.
Do wou mean BETWEEN 68 and 84?
the mean score in std 6 test was 72and the standard diviation was 9. calculate the z score for a pupil who scored 42
To determine the percentage of people with IQ scores between 68 and 84, we can use the 68-95-99.7 Rule, also known as the empirical rule or the three-sigma rule.
According to this rule, for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the mean IQ score is 100 and the standard deviation is 16, we can calculate the range within one standard deviation from the mean.
Lower limit of one standard deviation below the mean:
Mean - (1 * Standard deviation) = 100 - (1 * 16) = 84
Upper limit of one standard deviation above the mean:
Mean + (1 * Standard deviation) = 100 + (1 * 16) = 116
Therefore, IQ scores between 68 and 84 fall within one standard deviation below the mean.
Since we know that approximately 68% of the data falls within one standard deviation of the mean, we can conclude that approximately 68% of people would have an IQ score between 68 and 84.