$$ X $$ is a normally distributed random variable with mean 54 and standard deviation 13 . What is the probability that $$ X $$ is less than 25 ? Write your answer as a decimal rounded to the nearest thousandth.

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To find the probability that $$ X $$ is less than 25 for a normally distributed random variable $$ X $$ with mean $$ \mu = 54 $$ and standard deviation $$ \sigma = 13 $$, follow these steps:

1. **Standardize the Variable:**
   
   Convert $$ X $$ to a standard normal variable $$ Z $$ using the z-score formula:
   $$
   Z = \frac{X - \mu}{\sigma}
   $$
   For $$ X = 25 $$:
   $$
   Z = \frac{25 - 54}{13} = \frac{-29}{13} \approx -2.23
   $$

2. **Find the Cumulative Probability:**
   
   Using standard normal distribution tables or a calculator, find the cumulative probability $$ P(Z < -2.23) $$.

The cumulative probability for $$ Z = -2.23 $$ is approximately:
   $$
   P(Z < -2.23) \approx 0.013
   $$

3. **Conclusion:**
   
   The probability that $$ X $$ is less than 25 is **0.013** when rounded to the nearest thousandth.

**Answer:**  
0.013
The probability that $$ X $$ is less than 25 is **0.013**.

is a normally distributed random variable with mean 54 and standard deviation 13 .
What is the probability that is less than 25 ?
Write your answer as a decimal rounded to the nearest thousandth.

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is a normally distributed random variable with mean 54 and standard deviation 13 . What is the probability that is less than 25 ? Write your answer as a decimal rounded to the nearest thousandth.