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.

Question 1. On average, how many prescriptions would this pharmacist process until he or she made the first dispensing error? 25 (use 2 decimal places in your answer)

Question 2. What is the probability that the first dispensing error occurs among the first 6 prescriptions? (Use 3 decimal places in your answer)

Question 3.A new trainee pharmacist has an error rate of 0.11. 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 5 prescriptions. 9.09 expected number (use 2 decimal places in your answer) prob. first error is among first 5 prescriptions (use 3 decimal places).

Explanation / Answer

1) expected prescriptions =1/p =1/0.04 =25

2) probability that the first dispensing error occurs among the first 6 prescriptions =1-P(no error in first 6)

=1-(1-0.04)6 =1-0.7828 =0.2172

3)

i) expected number =1/0.11 =9.09

ii) let median be x: therefore P(X<=x) =0.5 =1-(0.96)x

0.96x =0.5

taking log and solving:

x =16.98 ~17

iii) prob. first error is among first 5 prescriptions =1-P(no error in first 5) =1-(0.89)5 =1-0.5584 =0.442

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