SOLUTION: Can you please help me with this? Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distribu

Question 153425: Can you please help me with this?
Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:
a) what is the probability that the drug will be effective for 2 hours or less?
b) what is the probability that the drug will be effective for 1 hour or less?
c) what is the probability that the drug will be effective for 3 hours or more?
I greatly appreciate all your help.
Julie
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:
------------------------
a) what is the probability that the drug will be effective for 2 hours or less?
Find the z-score for 2 hours:
z(2) = (2-2)/0.3 = 0
P(x <= 2) = P(z <= 0) = 0.5
------------------------------------
b) what is the probability that the drug will be effective for 1 hour or less?
Find the z-score for 1 hour:
z(1) = (1-2)/0.3 = -1/3
P(x <= 1) = P(z <= -1/3) = 0.36944..
--------------------------------------
c) what is the probability that the drug will be effective for 3 hours or more?
Find the z-score for 3 hours:
z(3) = (3-2)/0.3 = 1/3
P(x <= 3) = P(z <= 1/3) = 0.630559....
==============================================
Cheers,
Stan H.

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