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 probability that a test taker scores at least 70 points, we need to find the area under the normal curve to the left of 70 points.
Using the Z-score formula, we first find the Z-score for 70 points:
Z = (X - μ) / σ
Z = (70 - 100) / 15
Z = -30 / 15
Z = -2
Next, we look up the Z-score of -2 in the standard normal distribution table or use a calculator to find the corresponding area. The area to the left of Z = -2 is approximately 0.0228.
To find the probability of scoring at least 70 points, we subtract this area from 1:
P(X ≥ 70) = 1 - P(X < 70)
P(X ≥ 70) = 1 - 0.0228
P(X ≥ 70) = 0.9772
Therefore, approximately 97.72% of test takers score at least 70 points.