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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?

Respuesta :

Answer:

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

Step-by-step 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:

[tex]P(0.05<X<4.95)=P(\frac{0.05-2.5}{0.95}<\frac{X-\mu}{\sigma}<\frac{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\times0.9951)-1\\=0.9902[/tex]

*Use a z-table for the probability.

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

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