# Probability using Normal Distribution

Using the normal distribution, answer the following questions.

1. A pharmaceutical drug has mean effective duration of 10.4 hours with a standard deviation of two hours. In what percentage of the patients will the effectiveness of the drug be:

a) Greater than 13 hours?

b) At least 9 hours?

c) Between 11.8 and 14.6 hours?

2. The number of new prescriptions per month for Plavix is normally distributed with a mean of 21000 and a standard deviation of 4750.

a) What is the probability that there will be more than 24000 new prescriptions?

b) What is the probability that the number of new prescriptions per month will be between 22,000 and 24,000?

c) In a sample of 30 months, what is the probability that the number of new prescriptions will be less than 21500?

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#### Solution Preview

Please see the attached file.

1. A pharmaceutical drug has mean effective duration of 10.4 hours with a standard deviation of two hours. In what percentage of the patients will the effectiveness of the drug be:

a) Greater than 13 hours?

Mean=M = 10.4 hours

Standard deviation =s= 2.0 hours

x= 13.0 hours

z=(x-M )/s= 1.3 =(13-10.4)/2

Cumulative Probability corresponding to z= 1.3 is= 0.9032

Or Probability corresponding to x< 13.0 is Prob(Z)= 0.9032 0r= 90.32%

Therefore probability corresponding to x> 13.0 is 1-Prob(Z)= 0.0968 =1-0.9032

0r= 9.68%

Answer: 0.0968 or 9.68%

b) At least 9 hours?

At least 9 hours means greater than 9 hours

Mean=M = 10.4 hours

Standard deviation =s= 2.0 hours

x= 9.0 hours

z=(x-M )/s= -0.7 =(9-10.4)/2

Cumulative Probability ...

#### Solution Summary

Normal Distribution has been used for probability calculations.