In order to solve this problem, we will calculate the z-score of the given data.
To do this, we use the formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]We plug in the given data:
[tex]z=\frac{154-100}{19}\approx2.8421[/tex]With this z-score, we can consult a z-score probability table or use an online resource. However, this will give us
[tex]P(z<2.8421)[/tex]but we are interested in itbeing greater than it, so we must calculate
[tex]1-P(z<2.8421)=1-0.99776=0.00224[/tex]So, the percentage of the population that has an IQ above 154 is 0.224%.
