Normal Curve Problems Using the Empirical Rule
2. Perform calculations (show work)
Assume IQ is normally distributed with mean 100 points and standard deviation 15 points. What percent of test takers score at least 70 points? Use the sketch area to show your work and enter your answer below.
To find the percent of test takers scoring at least 70 points, we need to calculate the area under the normal curve to the left of 70 points and then subtract that area from 1 to get the area to the right of 70 points.
First, we need to standardize the score of 70 using the formula:
Z = (X - μ) / σ
Z = (70 - 100) / 15
Z = -30 / 15
Z = -2
Now, we look up the z-score of -2 on the standard normal distribution table to find the area to the left of -2, which is approximately 0.0228.
Therefore, the area to the right of 70 points is:
1 - 0.0228 = 0.9772
Therefore, approximately 97.72% of test takers score at least 70 points.