Statistics Problem

Question

Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is 10 milligrams. 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 = 10 milligrams and standard deviation 𝜎 = 1.6 milligrams. If a clinical overdose is defined as a dose larger than 14 milligrams, what is the probability that a patient will receive an overdose?

Answer 1

let x be dose, where x is normally distributed with mean = 10 and std dev = 1.6.

want to find P(x > 14).

can standardize x to z value by subtracting mean and dividing by std dev:

P(z > (14 - 10)/1.6) = P(z > 2.5)

Since the normal distribution curve is symmetric, that is the same as:

P(z < -2.5), which from the tables is 0.0062