# At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo.

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1245 with a standard deviation of 32 years. The distribution of dates was more or less moundshaped and symmetrical about the mean. Use the empirical rule to estimate the following. (a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between and A.D. (b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found between and A.D. (c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found between and A.D. A person’s blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean ? = 88 and standard deviation ? = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 140 (borderline diabetes starts at 140)