Does anybody know this ?
1 answer:
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Answer:
0.15%
Step-by-step explanation:
We have been given that IQ scores have a bell-shaped distribution with a mean of 97 and a standard deviation of 12. We are asked to find the percentage of IQ scores that are greater than 133 using the empirical rule.
First of all, we will find z-score for given sample score of 133 as z-score tells us a data point is how many standard deviation away from mean.
, where,
= Z-score,
= Sample score,
= Mean,
= Standard deviation.
We know that according to the empirical rule 68% of data lies within one standard deviation of mean, 95% of data lies within two standard deviation of mean and 99.7% of data lies within one standard deviation of mean.
Since 133 is 3 standard deviation above mean, so 0.3% lies above and below 3 standard deviation.
Since we need IQ scores above 133, so we will divide 0.3% by 2 as:
Therefore, 0.15% of IQ scores are greater than 133.