Page 30 - Reference Guide For Foreign Pharmacy Licensing Exam Theory

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To calculate the mean in binomial distribution, one should use the following formula:

Mean = n x p where p = probability of success and n = number of trials.

Example: Calculate the mean in binomial distribution, if 100 patients were treated with an antibiotic
which has a cure rate of 80%.

Mean = n x p
= 100 x 0.8
= 80

Thus, if 100 patients were treated with the antibiotic which has a cure rate of 80%, one can say that 80
patients will be cured out of 100 treated patients on an average.

The standard deviation in binomial distribution can be calculated by using the following equation:

SD = √ (1− ) Where q = 1 – p (p + q = 1)

Example: SD of proportions of patients (p= 0.8) cured out of 100 treated would be:

SD = √ 0.8 (1−0.8) = 0.04 or 4%.
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Thus, one can say that out of 100 treated patients, on an average 80 patients would be cured with
a standard deviation of + 4 from the mean. Therefore at any given time one can expect to cure 76 to 84
(80 + 4) patients out of 100 treated patients.

The Normal Distribution:

The normal distribution can be considered as the underlying foundation of statistical theories and their
applications.

The mean of a normal distribution can be + or - but the SD must be positive.

The standard normal distribution must have the standard normal curve to calculate the probability.

Example: Calculate the probability of value falling between -0.4 and + 1.2 [The area corresponding to Z(-
0.4) = 0.655 and Z(1.2) = 0.884]

The difference is (0.884 - 0.665) = 0.229. Thus the probability of observing a value between -0.4 and 1.2
is 0.229.

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