In the article Geometric Probability Distribution for Modeling of Error Risk Dur

Question

In the article Geometric Probability Distribution for Modeling of Error Risk During Prescription Dispensing, American Journal of Health-System Pharmacists, Vol. 63, Issue 11, June 1 2006, the authors use the geometric model to analyze how many prescriptions a pharmacist can process until the pharmacist makes the first dispensing error, either in labeling (incorrect information or instructions) or drug content (omissions; incorrect drug, quantity, or strength). Use this Excel file geometric probabilities (enable the macro after opening the file) or this Excel file geometric probabilities 2 to assist you with the geometric probability calculations required to answer the questions below. Suppose a pharmacist's error rate is 0.04.

What is the probability that the first dispensing error occurs among the first 16 prescriptions?

A new trainee pharmacist has an error rate of 0.19. Find the expected number of prescriptions until the first dispensing error, the median number of prescriptions until the first dispensing error, and the probability that the first dispensing error occurs among the first 6 prescriptions.

expected number (use 2 decimal places in your answer)?
prob. first error is among first 6 prescriptions (use 3 decimal places)?

Explanation / Answer

1 probability that the first dispensing error occurs among the first 16 prescriptions =1-P(no error in first 16)

=1-(1-0.04)16 =1-0.5204 =0.4796

2)

for new trainee

a) expected number of prescriptions until the first dispensing error =1/p =1/0.19 =5.263

b) median number of prescriptions =1-(1-0.19)x =0.5

0.81x =0.5

taking log on both sides ; x =3.29

c)  prob. first error is among first 6 prescriptions =1-P(no error in first 6) =1-(1-0.19)6 =0.718

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