Can y\'all please solve problem 1.20 from the book Manufacturing Systems Modelin

Question

Can y'all please solve problem 1.20 from the book Manufacturing Systems Modeling and Analysis (shown below in 2 pics)?

For some reason it doesn't appear on the step-by-step solutions available on the website...

Thank you!

1.20. The purpose of this problem is to illustrate the dangers of statistics, espe- cially with respect to categorical data and the use of conditional probabilities. In this example, the data may be used to support contradicting claims, depending on the inclinations of the person doing the reporting! The population in which we are interested is made up of males and females, those who are sick and not sick, and

Explanation / Answer

Answer:

Based on the given data:

a) What is the conditional probability of being sick given that the treatment was received and the patient is a male?

Total population (Male + Female) =600 + 720 = 1320

Total Male = 600

Probability of male P(M) = 600/1320

Probability of being sick given that the treatment was received (male patient) = 200/600

Probability of being sick P(S), given that the treatment was received and the patient is a male is:

(200/600) / (600/1320) = 200/1320 = 0.1515

b) Considering only the population of males, should the treatment be recommened?

Male sick treated probability = 200/600 = 0.333

Male Treated Not sick probability = 300/600 = 0.500

Since patients that received treatment prior to becoming sick are less in proportion compared to patients that didnot received treatment, therefore considering only the male population, they should receive treatment.

c) Considering only the population of females, should the treatment be recommended?

Female sick treated probability = 50/720 = 0.333

Female Treated Not sick probability = 100/720 = 0.139

Since patients that received treatment prior to becoming sick are more in proportion compared to patients that didnot received treatment, therefore considering only the female population, they should not receive treatment.

d) Considering the entire population, should the treatment be recommended?

Males Sick Not Sick Total Treated 200 300 500 Not Treated 50 50 100 Total 250 350 600

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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