Math Problem Statement

If bolt thread length is normally distributed, what is the probability that the thread length of a randomly selected bolt is

a. Within 1.5 SDs of its mean value?

b. Farther than 2.5 SDs from its mean value?

c. Between 1 and 2 SDs from its mean value?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Normal Distribution
Z-scores

Formulas

P(-z ≤ Z ≤ z)
Cumulative probability for a standard normal distribution
P(Z > z) = 1 - P(Z ≤ z)

Theorems

Empirical Rule (68-95-99.7 Rule)
Standard Normal Distribution

Suitable Grade Level

Grades 10-12