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...

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="">