For a 95% confidence interval for a population mean,there is ________.

A) a 95% confidence that the center of the interval is the true population mean
B) a 95% probability that the true population mean will fall in that range of values
C) a 95% probability that the population mean comes from a normal distribution
D) a 95% confidence that the sample mean is the true population mean

A confidence interval is based on the concept of sampling variability, which is the variation in sample statistics (such as the sample mean) from sample to sample due to chance. A 95% confidence interval means that if we repeated the sampling process many times and constructed a confidence interval for each sample, about 95% of those intervals would contain the true population mean. Therefore, there is a 95% probability that the true population mean will fall in that range of values, but we cannot say with certainty that the center of the interval is exactly equal to the true population mean.