A researcher measures the blood pressure for a sample of 10,000 men. She observes that the diastolic blood pressure is normally distributed with mean 80 mm Hg and standard deviation 10 mm Hg. a. What fraction of the men in this sample have diastolic blood pressure between 65 and 95 mm Hg? b. For this sample, the first quartile Q1 equals 73.3 mm Hg and the third quartile Q3 equals 86.7 mm Hg. In the boxplot section, an outlier was defined as any data point that is less than Q1 1.5 IQR or greater than Q3 + 1.5 IQR (where the interquartile range IQR = Q3 Q1). Using this definition of outliers and the fact that the sample is normally distributed, what fraction of men in this sample have diastolic blood pressure measurements that are outliers? c. Take a random sub-sample of 100 men from this sample. What is the probability the sample mean of the diastolic blood pressure for these 100 men is between 78.5 and 81.5 mm Hg?