1. Draw and label curve (including µ, σ, ticks, shading)
2. Perform calculations (show work)
3. Answer the question with context
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.
1.
Curve sketch:
- Mean (µ) = 100 points
- Standard deviation (σ) = 15 points
Tick marks:
- 70 points
- Shaded area to the left of 70 points
Shading:
- Shading area to the left of 70 points
2. Calculations:
To find the percentage of test takers who score at least 70 points (P(X ≥ 70)), we need to find the area to the right of 70 points.
Z = (X - µ) / σ
Z = (70 - 100) / 15
Z = -2
Using a standard normal distribution table or calculator, the area to the right of Z = -2 is approximately 0.9772.
Therefore, the percentage of test takers scoring at least 70 points is 1 - 0.9772 = 0.0228, or 2.28%.
3. Answer:
Approximately 2.28% of test takers score at least 70 points on the IQ test.