$$ X $$ is a normally distributed random variable with mean 58 and standard deviation 2 . What is the probability that $$ X $$ is greater than 60 ? 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 determine the probability that $$ X $$ is greater than 60, where $$ X $$ is normally distributed with a mean ($$ \mu $$) of 58 and a standard deviation ($$ \sigma $$) of 2, we can use the **68-95-99.7 rule** (also known as the empirical rule).

1. **Identify the Z-score:**
   $$
   Z = \frac{X - \mu}{\sigma} = \frac{60 - 58}{2} = 1
   $$
   So, 60 is 1 standard deviation above the mean.

2. **Apply the 68-95-99.7 Rule:**
   - **68%** of the data falls within **±1** standard deviation from the mean.
   - Therefore, the probability that $$ X $$ is **less than or equal to 60** is roughly **68% / 2 = 34%** above the mean.
   - The total area under the curve is 100%, so the probability that $$ X $$ is **greater than 60** is:
     $$
     50\% - 34\% = 16\%
     $$
   
3. **Convert to Decimal:**
   $$
   16\% = 0.16
   $$

**Final Answer:**  
The probability that $$ X $$ is greater than 60 is **0.160**.
The probability that $$ X $$ is greater than 60 is **0.160**.

is a normally distributed random variable with mean 58 and standard deviation 2 .
What is the probability that is greater than 60 ?
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 58 and standard deviation 2 . What is the probability that is greater than 60 ? Use the rule and write your answer as a decimal. Round to the nearest thousandth if necessary.