A researcher wants to estimate the mean age of newly diagnosed type II diabetes mellitus patients in a certain adult population. From a sample of 100 subjects, the mean age at diagnosis was 45.8 years and the population standard deviation is 12.5 years. If the population from which the sample was drawn follows a normal distribution. It is desired to prove that the mean age of diagnosis of these patients is different from 50 years through a confidence interval, with a 1% significance. What would be the most suitable interval estimate for this analysis?

Options:

a. (43.35, 47.05)

b. (38.05, 53.55)

c. (43.35, 48.25)

d. (32.95, 58.65)