Answer to Question #87853 in Statistics and Probability for Denver Cooper

Question

The level of potassium present in the blood of an adult person is normally distributed with mean 3.8 and standard deviation 0.2. A person is chosen at random:
a) (4) What is the probability that the person's potassium level is greater than 4.1?
b) (3) If the potassium level is less than 3.4, it is said that the person suffers from hypocalcemia. What is the probability that a person suffers from this disease?
c) (5) What is the probability that the potassium level is greater than 3.25 but less than 3.75?
d) (6) People with the lowest 15% of potassium level will be subjected to a diet to raise the level. What should be the maximum level of potassium required to be subjected to the diet?

Answer 1

a) P(X>4.1)=p(Z>(4.1-3.8)/0.2)=P(Z>1.5)=1-P(Z<1.5)=0.0668.

b) P(X<3.4)=P(Z<(3.4-3.8)/0.2)=P(Z<-2)=0.0228.

c) P(3.25<X<3.75)=P((3.25-3.8)/0.2<Z<(3.75-3.8)/0.2)=P(-2.75<Z<-0.25)=P(Z<2.75)-P(Z<0.25)=0.3983.

d) P(Z<z)=0.15 -> z=-1.04 -> x=3.8-1.04*0.2=3.59