Question

iq scores of people around the world are normally distributed, with a mean of 100 and a standard deviation of 15. what is the probability that a random person would score less than 127? options: 1.1527, 0.9648, 0.8849, 0.2417

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 122$, $\mu=100$, and $\sigma = 15$.
$z=\frac{122 - 100}{15}=\frac{22}{15}\approx1.47$.

Step2: Find the probability

We use the standard normal distribution table (z - table). Looking up the value of $z = 1.47$ in the z - table, we find that the cumulative probability $P(Z<1.47)$ is approximately $0.9292$.

Answer:

The probability that a randomly - selected person would score less than 122 is approximately $0.9292$. Since the closest option to $0.9292$ among the likely options (not shown fully in the image but based on the calculation) is likely to be the correct one. If we assume the options are in decimal form, the closest value to $0.9292$ should be chosen.