Question

Central Eye Clinic advertises that 90% of its patients approved for LASIK surgery to correct vision problems have successful surgeries.
a). In the random-number table, assign the digits 0 through 8 to the event "successful surgery" and the digit 9 to the event "unsuccessful surgery." Does this assignment of digits simulate 90% successful outcomes?

b). Use the random-digit assignment model of part (a) to simulate the outcomes of 15 trials begin at column 1, line 2.

c). In the random-number table, assign the digits 1 through 9 to the event "successful surgery" ansd the digit 0 to the event "unsuccessful surgery." Does this assignment of digits simulate 90% successful outcomes? Using this, repeat part (b).

d). What makes up a trial? What is a success? What is a failure? What are the values of n, p an q?

Answer 1

The key to your answer is in d): What is a success? What is a failure? 
If a patient was -6.0 diopters and after Lasik was -1.00 diopter, most surgeons and those in the industry would consider this a failure. The patient, however, may consider it a success because at age 50 she does not need to use reading glasses and still qualifies for a driver's license with 20/40 distance vision.. A patient who can make out the Snellen 20/20 line - familiar letters in black on a white background in a controlled lighting environment - may be considered by the doctor a success, but the patient does not have the crispness of vision experienced before Lasik and with glasses. 
The nonprofit patient advocacy USAEyes.org took a different approach. Success of Lasik means that the patient received what was expected - no matter the numbers. Using a scale of Much Worse Than Expected, Worse Than Expected, As Expected, Better Than Expected, and Much Better Than Expected, the USAEyes Competence Opinion Reletave to Expectations (CORE) patient survey found: 
99% report quality of life as expected, better, or much better 98% day vision as expected, better, or much better 98% no complications or issues are seldom problematic 98% would recommend surgery to family and friends. 97% would have surgery again, knowing what they know now 96% wear corrective lenses as often as expected, less, or much less than expected 96% report postop vision without lenses as expected, better, or much better than expected when compared to preop vision with lenses 96% report overall quality of vision as expected, better, or much better than expected 91% no complications at any time 91% night vision as expected, better, or much better 7% complications seldom problematic – yet 91% of these same patients would have surgery again 2% complications frequent or always problematic – yet 22% of f these same patients would have surgery again