Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Letxbe a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles,xis approximately normally distributed with mean=37and standard deviation=13.Find the following probabilities. (Round your answers to four decimal places.)

(a)xis less than 60

(b)xis greater than 16

(c)xis between 16 and 60

(d)xis more than 60 (This may indicate an infection, anemia, or another type of illness.)

hickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of5.5millimeters (mm) and a standard deviation of0.9mm. For a randomly found shard, find the following probabilities. (Round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm

(b) the thickness is more than 7.0 mm

(c) the thickness is between 3.0 mm and 7.0 mm

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)1247with a standard deviation of44years.The distribution of dates was more or less mound-shaped and symmetric 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.