A technician is testing the consistency of a machine that cuts sheets of cardboard. The sample variance of the thickness of $20$ cardboard sheets is found to be $25{\text{ mm}}^2$. Assume the thickness values are normally distributed. Construct a $90\%$ confidence interval for both the population variance and the population standard deviation.

• A. For variance: $(16,47)$ For standard deviation: $(4,7)$
• B. For variance: $(4,7)$ For standard deviation: $(16,47)$
• C. For variance: $(18,45)$For standard deviation: $(4,7)$
• D. For variance: $(12,49)$For standard deviation: $(5,9)$

Answer: (A)