Question

The average lethal blood concentration of morphine is estimated to be 2.5 µg/mL with a standard deviation of 0.95 µg/mL. The data is normally distributed. Examine the range of values 0.05 to 4.95 µg/mL. Answer the following questions and provide the appropriate calculations (13 points):

a. What is the probability associated with the range lethal morphine blood levels?

Answer 1

The probability associated with the range lethal morphine blood levels is 0.9902.

Explanation:

Let X = lethal blood concentration of morphine.

The random variable X is normally distributed with parameter μ = 2.5 μg/ mL and σ = 0.95 μg/ mL.

Compute the probability of X within the range 0.05 to 4.95 μg/ mL as follows:

`P(0.05<X<4.95)=P((0.05-2.5)/(0.95)<(X-\mu)/(\sigma)<(4.95-2.5)/(0.95))\\=P(-2.58<Z<2.58)\\=P(Z<2.58)-P(Z<-2.58)\\=P(Z<2.58)-[1-P(Z<2.58)]\\=2P(Z<2.58)-1\\=(2*0.9951)-1\\=0.9902`

*Use a z-table for the probability.

Thus, the probability associated with the range lethal morphine blood levels is 0.9902.