Verified answer

This is a system of equations problem:

1 = (180 - μ) / σ

0.5 = (180 - 2μ) / σ

Solve both for σ:

σ = 180 - μ

σ = (180 - 2μ) / 0.5

Simplify the second equation:

σ = 180 - μ

σ = 360 - 4μ

Since they are both equal to σ, they are both equal to each other:

180 - μ = 360 - 4μ

Add 4μ to both sides:

180 + 3μ = 360

Subtract 180 from both sides:

3μ = 180

Divide both sides by 3:

μ = 60. Now we know the mean. Let's find the standard deviation:

σ = 180 - μ = 180 - 60 = 120

Answer: μ = 60 & σ = 120