Management of a golf ball company has carefully screened and selected 12 dozen golf balls, and it is agreed that this sample contains 15 nonconforming balls (all for various cosmetic reasons). The balls are given to an inspector for classification into "good" and "bad" piles. The inspector ends up rejecting 7 good balls, and accepting 6 bad balls. The inspector classifies the remaining balls in the sample correctly.
a. On average, what is the probability that this inspector will reject a golf ball? Enter your response rounded to three decimal places.
b. On average, what is the probability that this inspector will make a wrong decision? Enter your response rounded to three decimal places.
c. On average, what is the proportion of accepted units that are actually nonconforming? Enter your response rounded to three decimal places.© BrainMass Inc. brainmass.com October 25, 2018, 9:35 am ad1c9bdddf
Total Golf Balls = 12*12 = 144
Bad Balls = 15
Good Balls = 144 - 15 = 129
Balls Inspector Rejected: 7 good balls + [15-6 (accepted)] ...
A question on conditional probability
31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40
a. What is P(A B)?
b. What is P(A | B)?
c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusively they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.
d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
35. The US Bureau of Labor Statistics collected data on the occupations of workers 25 to
64 years old. The following table shows the number of male and female workers (in thousands) in each occupation category (Statistical Abstract of the United States:2002)
Occupation Male Female
Managerial/professional 19079 19021
Tech./Sales/Administrative 11079 19315
Service 4977 7947
Precision Production 11682 1138
Operators/Fabricators/Labor 10576 3482
Farming/Forestry/Fishing 1838 514
A. Develop a joint probability table.
B. What is the probability of a female worker being a manager or professional?
C. What is the probability of a male worker being in precision production?
D. Is occupation independent of gender? Justify your answer with a probability
37. A purchasing agent placed rush orders for a particular raw material with two different suppliers, A and B. If neither order arrives in four days, the production process must be shut down until at least one of the order arrives. The probability that supplier B can deliver the material in four days is .35
A. what is the probability that both suppliers will deliver the material in four days?
Because two separate suppliers are involved, we are willing to assume independence.
B. What is the probability that at least one supplier will deliver the material in four days.
C. What is the probability that the production process will be shut down in four days because of a shortage of raw material (i.e., both orders are lately)?