The angiogram is a standard diagnostic test used in clinical medicine to detect stroke in patients. This test has some risks for the patient, and several noninvasive techniques have been developed that are hoped to be as effective as the angiogram. One such method utilizes the measurement of cerebral blood flow (CBF) in the brain, since stroke patients tend to have lower levels of CBF than normal. Among healthy people, CBF is normally distributed with mean 75 and standard deviation 17. Patients are classified as being at risk for stroke if their CBF is below 40. What proportion of healthy patients will be mistakenly classified as being at risk for stroke? (Use the steps below.)

a. Draw a normal curve with the parameters as stated. Shade in the region in the figure that represents the proportion of healthy patients with a CBF below 40.

b. Convert the boundary of the region to a z-score. Round the answer to 2 decimal places.

c. Find the area that corresponds to the shaded region. Show the calculator function used and all inputs. Round the answer to 4 decimal places.