In the article Geometric Probability Distribution forModeling of Error Risk Duri

Question

In the article Geometric Probability Distribution forModeling 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 howmany prescriptions a pharmacist can process until the pharmacistmakes the first dispensing error, either in labeling (incorrectinformation or instructions) or drug content (omissions; incorrectdrug, quantity, or strength).

Use this Excel file geometricprobabilities to assist you with the geometric probabilitycalculations required to answer the questions below.

Suppose a pharmacist's error rate is 0.06.

Question 1. On average, how many prescriptionswould this pharmacist process until he or she made the firstdispensing error?
1

Question 2. What is the median number ofprescriptions until the pharmacist makes the first dispensingerror? Hint: Use the above geometric probabilitiesfile to find the smallest value of x such that P(X <= x) islarger than 0.50.
2

Question 3. What is the probability that thefirst dispensing error occurs among the first 7 prescriptions?
3 (Use 3 decimalplaces in your answer)

Question 4.A new trainee pharmacist has anerror rate of 0.16. Find the expectednumber of prescriptions until the first dispensing error, themedian number of prescriptions until the first dispensing error,and the probability that the first dispensing error occurs amongthe first 14 prescriptions.
4 expectednumber
5 mediannumber
6 prob. firsterror is among first 14 prescriptions (use3 decimal places).

Explanation / Answer

Suppose a pharmacist's error rate is 0.06.What is the probability that the first dispensing error occursamong the first 7 prescriptions? Answer: It is Geometric distribution. p=0.06 X~Geometric(p=0.06) P(X=x)={(1-p)^(x-1)}*p Thus, the probability is P(X=7)={(1-0.06)^6}*0.06=0.041

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