The quality assurance department at a hospital has as one of its responsibilitie

Question

The quality assurance department at a hospital has as one of its responsibilities the verification of medical records. One of the department's employees' samples medical records and checks each one for correctness. Historical data suggests that each medical record has a 0.84 probability of being correct. Suppose the employee begins checking medical records at some point in time. What is the probability that the 5th incorrect record is the 16th record checked? found? number of records checked until the 10th incorrect record is found? record incorrect record? checked? checked? at least 6 of the first 99 records are incorrect? incorrect records will be found in the first 102 records checked? a) b) On average, how many records will have been checked when the first incorrect record is c) Given that the 5th incorrect record is the 108th record checked, what is the expected d) What is the standard deviation of the number of records checked to find the 10th incorrect e) What is the probability that it requires checking more than 7 records to find the first f) What is the probability that there are exactly 5 incorrect records in the first 33 records g) What is the probability that there are exactly 3 incorrect records in the first 11 records h) Given that the 4th incorrect record is the 69th record checked, what is the probability that i Given that the 4th incorrect record is the 67th record checked, on average, how many

Explanation / Answer

Pr(Each medical record being correct) = 0.84

(a) Pr(5th incorrect record is the 16th checked record)

to calculate this we can say that out of starting 15 checked record 4 were incorrect and the 5th one is also incorrect

so, P (5th record is the 16th checked record) = 15C4 (0.16)4(0.84)11 * 0.16 = 0.1314 * 0.16 = 0.021

(b) As we have to find the average number of record to be checked when first incorrect record to be found.

Let say k is average number of record to be checked.

Pr(k) = (1-p)k-1p

so E[k] = 1/p = 1/0.16 = 6.25

(c) Here 5th record is incorrect is the 108th record checked. Expected number of records until the 10th incorrect record is found.

as geometric distribution has memoryless property.  That means that if you intend to repeat an experiment until the first success, then, given that the first success has not yet occurred, the conditional probability distribution of the number of additional trials does not depend on how many failures have been observed.

so E(10 th incorrect record is found) = (10-5) * (1/p) + 108 = 5 * (1/0.16) + 108 = 139.25

(d) Standard deviation of the number of records checked to find the 10th incorrect record.

Standard deviation s = (1-p)/ sqrt(p) = (1 - 0.16)/ sqrt (0.16) = 0.84/ 0.4 = 2.1

(E) Pr( it requires more than 7 records to find the first incorrect record) = 1 - Pr (We will find incorrect record in initial 6 records) = 1 - [ 1 - (1-0.84)6] = 0.3513

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.