Math Problem Statement

Stanford-Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16. Find the probability that a randomly selected person has an IQ test score of:

(c) Between 72 and 128. draw a graph to show the Z values

Solution

The graph above shows a standard normal distribution with the area between Z=1.75Z = -1.75 and Z=1.75Z = 1.75 shaded in light blue. This shaded region represents the probability that a randomly selected person's IQ lies between 72 and 128, which is approximately 91.98%.

Would you like further details or explanations? Here are five additional questions related to this topic:

  1. How do you calculate probabilities for values outside the standard deviation range?
  2. What is the probability of having an IQ above 128?
  3. How can Z-scores be used to compare different datasets?
  4. How do you interpret Z-scores in different contexts?
  5. Can the IQ distribution change over time or in different populations?

Tip: Z-scores help standardize data, allowing comparisons between different distributions.

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Math Problem Analysis

Mathematical Concepts

Probability
Normal Distribution
Z-scores

Formulas

Z = (X - μ) / σ
P(a < Z < b) = P(Z < b) - P(Z < a)

Theorems

68-95-99.7 Rule (Empirical Rule)
Properties of Normal Distribution

Suitable Grade Level

Grades 9-12