Math Problem Statement
Assume the random variable x is normally distributed with mean
muμequals=8787
and standard deviation
sigmaσequals=44.
Find the indicated probability.
P(7474less than<xless than<8585)
Solution
Given that is a normally distributed random variable with mean and standard deviation , we need to find the probability .
To solve this, we'll standardize the values of using the z-score formula:
Step 1: Calculate the z-scores
- For :
- For :
Step 2: Find the corresponding probabilities
Using standard normal distribution tables or a calculator:
- corresponds to a very small probability, typically near 0.0006.
- corresponds to a probability of approximately 0.3085.
Step 3: Compute the required probability
The probability is the
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Z-score
Formulas
Z-score formula: z = (x - μ) / σ
Theorems
Central Limit Theorem
Suitable Grade Level
Advanced High School / College
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