3. Suppose that before a section of a newly constructed highway pavement is accepted by the...
3. Suppose that before a section of a newly constructed highway pavement is accepted by the State Department of Highway, the thickness of a 25 cm pavement is inspected for specification compliance by taking ultrasonic readings. Each section will be accepted if the measured thickness is atleast 23 cm; otherwise, the entire section will be rejected or a imposed. Use the following notation: penalty will be G constructed thickness of pavement is atleast 23 cm. A ultrasonic measured thickness is atleast 23 cm. From past experience, 90% of constructed highway works by the same contractor were found to be in compliance with specifications, i.e. based on the contractor's past construction record, we may assume that 90% of his constructed pavement will have acceptable ultrasonic reading. P(A) = 0.9 The ultrasonic thickness determination is only 80 % reliable; i.e. there is a 20% chance that a conclusion based on the ultrasonic test may be erronebus. In other words, the probability of thickness actually being 23 cm when ultrasonic reading indicated 23cm - P(G|A) and P(GIA) are 0.80. What is the probability that a well constructed section of pavement (i.e. a pavement with thickness atleast 23 cm) will be accepted in the test (i.e. the ultrasonic measured thickness will be atleast 23 cm)? [20 points]