IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 . Out of a randomly selected 1450 people from the population, how many of them would have an IQ between 106 and 125, to the nearest whole number?
Answer
3. Calculate the number of people with IQ between 106 and 125: \[ 1450 \times 0.3944 \approx 571.86 \]
Step 1 ：1. Calculate the z-scores for 106 and 125: \[ z_1 = \frac{106 - 100}{15} \approx 0.4 \] \[ z_2 = \frac{125 - 100}{15} \approx 1.67 \]
Step 2 ：2. Use a standard normal distribution table or calculator to find the area under the curve between z-scores \(z_1\) and \(z_2\): \[ P(0.4 \le Z \le 1.67) \approx 0.3944 \]
Step 3 ：3. Calculate the number of people with IQ between 106 and 125: \[ 1450 \times 0.3944 \approx 571.86 \]
