\( X \) 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.

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