Final answer:
Approximately 572 students will be rejected based on an IQ score of at least 95.
Step-by-step explanation:
To find the number of students that will be rejected based on an IQ score of at least 95, we need to determine the area under the normal distribution curve below an IQ score of 95.
First, we calculate the z-score using the formula:
z = (X - μ) / σ
where X is the desired IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.
In this case, X = 95, μ = 115, and σ = 12.
Substituting these values into the formula, we have:
z = (95 - 115) / 12 = -20 / 12 ≈ -1.67
Next, we use the z-score to find the area under the normal distribution curve using a z-table or a statistical calculator.
The area to the left of the z-score is the probability that a student's IQ score is less than 95.
We can subtract this probability from 1 to find the probability that a student's IQ score is greater than or equal to 95.
The probability can be calculated as follows:
P(Z > -1.67) = 1 - P(Z < -1.67)
Using a z-table or a statistical calculator, we can find the area to the left of -1.67 is approximately 0.0475.
So the probability of a student's IQ score being greater than or equal to 95 is approximately 1 - 0.0475 = 0.9525.
To find the number of students that will be rejected based on an IQ score of at least 95, we multiply the probability by the total number of students:
Number of rejected students = 0.9525 * 600
≈ 571.5
Since we can't have a fraction of a student, we round up to the nearest whole number.
Therefore, approximately 572 students will be rejected based on an IQ score of at least 95.