Understanding the Normal Distribution
The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean (µ) and standard deviation (σ). In this case, the mean is given as 500.

Identifying the Standard Deviation (σ)
To find the standard deviation, we need to interpret the information that 60% of the values are greater than 600. This implies that 40% of the values are below 600.

Finding the Z-Score
Using the standard normal distribution table:
- A cumulative probability of 0.40 corresponds to a Z-score of approximately -0.25.
- This means that the value of 600 is 0.25 standard deviations above the mean.

Calculating the Standard Deviation (σ)
We can formulate the equation based on the Z-score:

Formula:
Z = (X - µ) / σ
Where:
- Z = -0.25 (Z-score for 600)
- X = 600
- µ = 500
Rearranging gives:
-0.25 = (600 - 500) / σ
This simplifies to:
-0.25σ = 100
Thus,
σ = 100 / -0.25 = 400
However, since standard deviation cannot be negative, we take the positive value:

Result:
- The standard deviation (σ) of the distribution is 400.

Conclusion
In summary, the normal distribution with a mean of 500 and 60% of values above 600 has a standard deviation of 400. Understanding these properties is crucial for statistical analysis in various fields, including UPSC exam preparation.