Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is μ. Because of the variations in the syringe, in reading the scale, and in mixing the fluid suspension, the actual dose administered is normally distributed with mean μ and variance σ2.
a. What is the probability that the dose administered differs from the mean μ by less than σ?
b. If X represents the dose administered, find the value of z so that P(X < μ + zσ) = 0.90.
c. If the mean dose is 10 mg, the variance is 2.6 mg2, and a clinical overdose is defined as a dose larger than 15 mg, what is the probability that a patient will receive an overdose?