Given:
Mean (μ) = 40
Standard Deviation (σ) = 5.1
Observations (n) = 100

To find:
Correct standard deviation after correcting the wrongly copied observation

Solution:
Step 1: Calculate the sum of all observations
The sum of all observations can be calculated using the formula:
Sum = Mean × Number of Observations
Sum = 40 × 100
Sum = 4000

Step 2: Calculate the sum of squared differences
The sum of squared differences can be calculated using the formula:
Sum of Squared Differences = Σ(xi - μ)^2
where xi is each observation and μ is the mean

Let's calculate the sum of squared differences for the given observations:
Observations: x1, x2, x3, ..., x99, x100

Sum of Squared Differences = (x1 - 40)^2 + (x2 - 40)^2 + (x3 - 40)^2 + ... + (x99 - 40)^2 + (x100 - 40)^2

Step 3: Calculate the corrected sum of squared differences
Since one observation was wrongly copied as 50 instead of 40, we need to correct this in the sum of squared differences calculation.

Considering the wrongly copied observation as xn (which should be 40), the corrected sum of squared differences can be calculated using the formula:
Corrected Sum of Squared Differences = Sum of Squared Differences - (xn - μ)^2 + (xn - correct value)^2

Substituting the values:
Corrected Sum of Squared Differences = Sum of Squared Differences - (50 - 40)^2 + (50 - 40)^2

Step 4: Calculate the corrected standard deviation
The corrected standard deviation can be calculated using the formula:
Corrected Standard Deviation (σ') = √(Corrected Sum of Squared Differences / (Number of Observations - 1))

Substituting the values:
Corrected Standard Deviation (σ') = √(Corrected Sum of Squared Differences / (100 - 1))

Step 5: Calculate the final value of the corrected standard deviation
Calculating the corrected standard deviation using the above formula will give us the final value.

Thus, the correct standard deviation can be found by following the above steps and substituting the given values into the formulas.