Submit your solutions in soft copy (Scanned copy or Word file) to the Blackboard
ID: 3174958 • Letter: S
Question
Submit your solutions in soft copy (Scanned copy or Word file) to the Blackboard before specified deadline. You can submit a Hard copy in our class, but you should have a soft copy just in case that your hard copy is missed. The soft copy will be used for the proof of your submission. The analysis of shafts for a compressor is summarized by conformance to specifications. If a shaft is selected at random, what is the probability that it conforms to surface finish requirements? What is the probability that the selected shaft conforms to surface finish requirements or to roundness requirements? What is the probability that the selected shaft either conforms to surface finish requirements or does not conform to roundness requirements? What is the probability that the selected shaft conforms to both surface finish and roundness requirements?Explanation / Answer
Total number of shafts = 334+15+12+9 = 370
Probability that selected shaft confirming to Surface Finish requirements :P(A) = Number Shafts confirming to Surface finish requirements/Total shafts
= (334+15)/371 = 349/370
P(A) =349/371
Probability that selected shaft confirming to Surface Finish requirements or to roundedness requirement
Probability that selected shaft confirming to roundedness requirement : P(B) = 346/370
Probability that selected shaft confirming to Surface Finish requirements or to roundedness requirement = P(A or B)
By Addition theorem P(A or B) = P(A) + P(B) -P(A and B)
P(A and B) = Probability that selected shaft confirming to Surface Finish requirements and to roundedness requirement = 334/370
P(A or B) = P(A) + P(B) -P(A and B) = 349/370 + 346/370 - 334/370 = 361/370
Probability that selected shaft either confirms to Surface Finish requirements or does not conform roundedness requirement =P( A or B') ( B' is complement of B)
P( A or B') = P(A) + P(B') - P(A and B')
P(B') = 1-P(B) = 1-346/370 = 24/370
P(A and B') = Probability that selected shaft either confirms to Surface Finish requirements and does not conform roundedness = 15/370
P( A or B') = P(A) + P(B') - P(A and B') = 349/370 + 24/370 - 15/370 = (349+24-15)/370 = 358/370
Probability that selected shaft either confirms to Surface Finish requirements or does not conform roundedness requirement =P( A or B') = 358/370
d)Probability that selected shaft either confirms to both Surface Finish requirements and roundedness requirement =P(A and B)
P(A and B) = Probability that selected shaft confirming to Surface Finish requirements and to roundedness requirement = 334/370
Roundness Confirms Yes No Total Surace Finish Confirm Yes 334 15 349 No 12 9 21 Total 346 24 370