Question

directions answer the questions below to check your understanding and move forward in the course! this quiz is not graded. given the mean score of an iq test is 100 with a standard deviation of 10, what is the probability that a person would score 130 or higher? select the correct answer 13.5% 47.5% 0.15% 2.35%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 130$, $\mu=100$, and $\sigma = 10$. So, $z=\frac{130 - 100}{10}=\frac{30}{10}=3$.

Step2: Use the standard normal distribution

The total area under the standard - normal curve is 1. The area between $z=- 3$ and $z = 3$ is approximately 0.997. The area outside of $z=-3$ and $z = 3$ is $1 - 0.997=0.003$. Since the normal distribution is symmetric, the area to the right of $z = 3$ is $\frac{0.003}{2}=0.0015$ or $0.15\%$.

Answer:

0.15%