A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is​ faster: the​ men's marathon winner or the​ women's wheelchair marathon​ winner, on average. A paired​ t-test was performed on data from a random selection of 15 of the marathons to determine if there was evidence to indicate that the​ women's winning wheelchair time is faster than the​ men's winning running​ time, on average. What must be true about the population of differences in the​ women's wheelchair winning times and​ men's winning times at this marathon for conclusions from the paired​ t-test to be​ valid? Choose the correct answer below. A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample​ and/or if the population of differences in winning times for all years is normal. B. Because there were at least 5 years of​ observations, 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 years will be normal. D. Because of the small sample size of differences in winning times between the​ women's wheelchair winner and the​ men's running​ winner, the distribution of sample means of the differences cannot be normal.