Suppose that we measure the systolic blood pressure of n = 15 random Type I Diabetes patients. A 95% Student's t confidence interval for the population mean blood pressure is (115.87, 122.73).

a)The sample mean and standard deviation are

A: x = 115.87, s = 1.60.

B: x = 119.30, s = 1.60.

C: x = 119.30, s = 6.19.

D: x = 119.30, s = 6.98.

E: Impossible to determine based on this information.

b) What important assumption is required for the confidence interval to be valid.

A: The sample mean is an unbiased estimator of the population mean.

B: The distribution of systolic blood pressure in the population follows a Student's t distribution.

C: The population standard deviation is known.

D: The distribution of systolic blood pressure in the population follows a normal distribution.

E: n = 15 is a large sample size for this population.