Respuesta :
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.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]z[/tex] = Z-score,
[tex]x[/tex] = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
[tex]z=\frac{133-97}{12}[/tex]
[tex]z=\frac{36}{12}[/tex]
[tex]z=3[/tex]
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:
[tex]\frac{0.3\%}{2}=0.15\%[/tex]
Therefore, 0.15% of IQ scores are greater than 133.
