Ultrasonic testing is performed every 110 mile along a new s

Ultrasonic testing is performed every 1/10 mile along a new section of highway to ensure that the pavement is thick enough. Each 1/10th mile section is judged to be in compliance with Missouri Department of Transportation (MODOT) specifications if its measured thickness, t, is greater than or equal to 7.5 inches, otherwise, the section is rejected. Past experience indicates that 90% of all sections are accepted as in compliance based on the test. However, the ultrasonic thickness measurement is known to be only 80% reliable, so that there is a 20% chance that the measured thickness is erroneous. a) What is the probability that a particular section of pavement meets the specifications AND will be accepted by MODOT? will be accepted on the basis of the ultrasonic measurement? the ultrasonic measurement? b) What is the probability that a section is poorly constructed (i.e., its thickness is too low), but it c) What is the probability that if a section is constructed properly, it will be accepted on the basis of

Solution

Ans- a) Probability= .90 (Given- 90% meet the specifications and get accepted)

b) Probability= .20 (Given- the ultrasonic thickness test to be 20% erroneous)

c) Probability= .80 (Given- the ultrasonic thickness test to be 80% relaible)