Question

In: Statistics and Probability

A sample of 400 patients from a group medical plan received treatment from either a physician or a nurse practitioner.

A sample of 400 patients from a group medical plan received treatment from either a physician or a nurse practitioner.   Their medical care was then rated as satisfactory or unsatisfactory. Answer the questions based on the results summarized in the table below:   


PhysicianNurse PractitionerTotal
Satisfactory90161251
Unsatisfactory37112149
Total127273400

  

A.   Are the events Physician and Nurse-Practitioner mutually exclusive? Explain why or why not.

B.   What is the probability that a patient received treatment that was Satisfactory and from a Physician?

C.   What is the probability that a patient received treatment that was from a Physician or was Satisfactory?

D.   What is the probability that a patient received Satisfactory treatment, given that the patient was treated by a Nurse Practitioner?

E. Are the events Physician and Satisfactory independent events?Compare probabilities to decide, and explain your reasoning using one of these phrases: equally likely, more likely, less likely.

Solutions

Expert Solution

a) There is no one in the table who is both a physicial, and a nurse practitioner, therefore Yes the 2 events are mutually exclusive.

b) The probability that the treatment was satisfactory and from physician is computed here as:

= 90 / 400

= 0.225

Therefore 0.225 is the required probability here.

c) Probability that it is from a physicial or satisfactory is computed here as:

= (251 + 127 - 90 ) / 400

= 288 / 400

= 0.72

Therefore 0.72 is the required probability here.

d) Given that the patient was treated by a nurse practitioner, probability that it was satisfactory is computed as:

= 161 / 273

= 0.5897

Therefore 0.5897 is the required probability here.

e) P( physician ) = 127 / 400 = 0.3175
P( satisfactory ) = 251 / 400 = 0.6275

P( satisfactory and physician ) = 90 / 400 = 0.225
P( physician ) P( satisfactory ) = 0.3175*0.6275 = 0.1992 which is not equal to 0.225

Therefore the 2 events are not independent .


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