A manufacturer of large appliances must decide which of two​ machines, A and​ B, they want to purchase to perform a specific task in the production process. The goal is to buy the machine that has smaller mean time required to perform the task. The plant supervisor selects 15 machine operators at​ random, and each operator performs the task on each of the two machines. The production times are paired for each worker. A paired​ t-test is to be performed to determine if there is evidence that the population mean time using machine A is less than the population mean time using machine B. The summary statistics for the differences in the times required for the task in minutes​ (machine A​ - machine​ B) for the 15 randomly selected workers are given below. n=15; x̅ = -10.9 and s=20.3

What must be true about the population of differences in the times required for the task between machine A and machine B for conclusions from the paired t-test to be valid for the population of differences among all workers?

a. Because of the small sample size of differences in times required between machine A and machine B, the distribution of sample means of the differences cannot be normal.
b. Because there were a total of 30 obervations (15 times from machine A and 15 times from machine B), the distribution of sample means of the differences will be approximately normal by the Central Limit Theorem.
c. Because the sample size is "large" enough, the distribution of differences for all workers will be normal.
d. Because of the small sample size of differences in times required between machine A and machine B, the distribution of differences for all workers must be normal.