Question

12 multiple choice 6.67 points from the same scenario as before: a genius is someone with an iq at least 140. what percent of the population is considered genius? (del mismo escenario que antes; un genio es alguien con un coeficiente intelectual de al menos 140. ¿qué porcentaje de la población se considera genio?) 38% 0.038% 38% el problema eres tu mr. r 3.8% previous

Explanation:

Step1: Assume IQ scores follow a normal distribution with mean $\mu = 100$ and standard - deviation $\sigma= 15$.

We want to find $P(X\geq140)$ where $X$ represents IQ scores.

Step2: Calculate the z - score.

The z - score formula is $z=\frac{x-\mu}{\sigma}$. Substituting $x = 140$, $\mu = 100$ and $\sigma = 15$, we get $z=\frac{140 - 100}{15}=\frac{40}{15}\approx2.67$.

Step3: Use the standard normal distribution table.

The standard normal distribution table gives $P(Z < 2.67)$. Looking up in the table, $P(Z < 2.67)\approx0.9962$. Since $P(X\geq140)=P(Z\geq2.67)=1 - P(Z < 2.67)$.
So $P(Z\geq2.67)=1 - 0.9962 = 0.0038$ or $0.38\%$.

Answer:

0.38%