Williams, Dunsiger, Jennings, and Marcus (2012) conducted a study to test how enhanced mood during exercise can increase the likelihood of physical activity in the future. They reported that at 6 months of physical activity, mood scores (rated on a scale from −5 to +5) after a walking exercise were 3.3 ± 1.2, and at 12 months, mood scores after a walking exercise were 3.3 ± 1.3 (mean ± standard error). Assuming these data are normally distributed, use the steps to conduct a z transformation to determine the following probabilities:
(a) What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) at 6 months of physical activity?
(b) What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) at 12 months of physical activity?