Problem:
Measurement error that is normally distributed with a mean of 0 and a standard deviation of 0.5 grams is added to the true weight of a sample. Then the measurement is rounded to the nearest gram. Suppose that the true weight of a sample is 165.5 grams.
Requirement:
Question 1: What is the probability that the rounded result is 167 grams?
Question 2: What is the probability that the rounded result is 167 grams or more?
Note: Explain the solution in detail.