91Ó°ÊÓ

Find the \(z\) value described and sketch the area described. Find \(z\) such that \(97.5 \%\) of the standard normal curve lies to the left of \(z\)

Find the \(z\) value described and sketch the area described. Find \(z\) such that \(5 \%\) of the standard normal curve lies to the right of \(z\).

Find the \(z\) value described and sketch the area described. Find the \(z\) value such that \(98 \%\) of the standard normal curve lies between \(-z\) and \(z\).

Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let \(x\) be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults, \(x\) is approximately normally distributed with mean \(\mu=38\) and standard deviation \(\sigma=12\) (see reference in Problem 25). What is the probability that (a) \(x\) is less than 60 ? (b) \(x\) is greater than \(16 ?\) (c) \(x\) is between 16 and 60 ? (d) \(x\) is more than 60 ? (This may indicate an infection, anemia, or another type of illness.)

Let \(z\) be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve. $$ P(z \leq 0) $$