Final answer:
To find the number of students with IQs above 140, calculate the area under the normal distribution curve to the right of 140. Use the z-score formula and a standard normal distribution table or calculator to find the area. Multiply the area by the total number of students to find the approximate number of students with IQs above 140.
Step-by-step explanation:
To find the number of students with IQs above 140, we need to calculate the area under the normal distribution curve to the right of 140.
We can use a z-score to find the area. The formula for the z-score is: z = (x - µ) / σ, where x is the value we want to find the probability for, µ is the mean of the distribution, and σ is the standard deviation.
First, calculate the z-score for 140 using the formula: z = (140 - 104) / 16 = 2.25.
Next, use a standard normal distribution table or a calculator to find the area to the right of 2.25. The area is approximately 0.0122.
Finally, multiply the area by the total number of students to find the approximate number of students with IQs above 140: 0.0122 x 52,000 = 634.4.
Therefore, approximately 634 students would have IQs above 140.