1. (5 points) Which distribution is used to perform inference on the mean when the standard deviation of the population is unknown?

A. The binomial distribution

B. The normal distribution

C. The t-distribution

D. The uniform distribution

E. The continuous distribution

2. (5 points) Construct a 95% confidence for the magnitude of an earthquake from a sample of14 earthquakes with a mean magnitude of 2.926 and standard deviation magnitude of 0.083on the Richtor scale.

(a) What are the lower and upper limits of the confidence interval?

(b) What is the margin of error of the magnitude estimate?

(c) Write a statement that interprets the confidence interval.

Please explain with work