To solve for the margin of error:
margin of error = critical value x standard error
To compute for the critical value:
1. compute alpha: α= 1 - (confidence level/100) = 1 - .99 = 0.01
2. Find the critical probability: p = 1 - α/2 = 1 - (0.01/2) = 0.995
3. Look for the z score at the z table, in this case it is 2.58. This is your critical value.
To compute for the standard error, the formula is:
standard error = standard deviation (σ) divided by √n = 1.6 / √420 = 0.0781
Now plug in the following in the formula:
margin of error: 2.58 * 0.0781 = 0.2014 or 0.20
The answer is letter C.
