$$ X $$ is a normally distributed random variable with mean 50 and standard deviation 10 . What is the probability that $$ X $$ is less than 30 ? Use the $$ 0.68-0.95-0.997 $$ rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

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To find the probability that $$ X $$ is less than 30, where $$ X $$ is normally distributed with a mean ($$ \mu $$) of 50 and a standard deviation ($$ \sigma $$) of 10, we can use the $$ 68-95-99.7 $$ rule (also known as the empirical rule).

1. **Identify the number of standard deviations from the mean:**
   $$
   30 = \mu - 2\sigma = 50 - 2(10) = 50 - 20 = 30
   $$
   So, 30 is 2 standard deviations below the mean.

2. **Apply the $$ 68-95-99.7 $$ rule:**
   - Approximately **68%** of the data lies within **±1** standard deviation from the mean (40 to 60).
   - Approximately **95%** of the data lies within **±2** standard deviations from the mean (30 to 70).
   - Approximately **99.7%** of the data lies within **±3** standard deviations from the mean (20 to 80).

3. **Calculate the probability:**
   - Since 95% of the data lies between 30 and 70, the remaining 5% is split equally in the two tails of the distribution.
   - Therefore, the probability that $$ X $$ is less than 30 is:
     $$
     P(X < 30) = \frac{5\%}{2} = 2.5\% = 0.025
     $$

**Final Answer:**  
The probability is 0.025.
The probability that $$ X $$ is less than 30 is 0.025.

is a normally distributed random variable with mean 50 and standard deviation 10 .
What is the probability that is less than 30 ?
Use the rule and write your answer as a decimal. Round to the nearest
thousandth if necessary.

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is a normally distributed random variable with mean 50 and standard deviation 10 . What is the probability that is less than 30 ? Use the rule and write your answer as a decimal. Round to the nearest thousandth if necessary.