Math Problem Statement

We are given a normally distributed random variable X with µ = 75 and σ = 5.

Find P (X > 85).

Find k such as P(X<k) = 0.997. Interpret your result.

Find the two values where the middle 68.27% of the distribution of X lie.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability
Normal Distribution
Standard Normal Distribution

Formulas

Z = (X - µ) / σ
P(X > 85) = P(Z > 2)
k = Z * σ + µ

Theorems

68-95-99.7 Rule (Empirical Rule)

Suitable Grade Level

College-level Statistics