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Bridge inspection ratings. According to the National
Chapter 4, Problem 55E(choose chapter or problem)
Problem 55E
Bridge inspection ratings. According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated every 2 years. The NBIS rating scale ranges from 0 (poorest rating) to 9 (highest rating). University of Colorado engineers used a probabilistic model to forecast the inspection ratings of all major bridges in Denver (Journal of Performance of Constructed Facilities, Feb. 2005). For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.
a. Use the forecast to find the probability that in a random sample of 10 major Denver bridges, at least 3 will have an inspection rating of 4 or below in 2020.
b. Suppose that you actually observe 3 or more of the sample of 10 bridges with inspection ratings of 4 or below in 2020. What inference can you make? Why?
Questions & Answers
QUESTION:
Problem 55E
Bridge inspection ratings. According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated every 2 years. The NBIS rating scale ranges from 0 (poorest rating) to 9 (highest rating). University of Colorado engineers used a probabilistic model to forecast the inspection ratings of all major bridges in Denver (Journal of Performance of Constructed Facilities, Feb. 2005). For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.
a. Use the forecast to find the probability that in a random sample of 10 major Denver bridges, at least 3 will have an inspection rating of 4 or below in 2020.
b. Suppose that you actually observe 3 or more of the sample of 10 bridges with inspection ratings of 4 or below in 2020. What inference can you make? Why?
ANSWER:
Step 1 of 3
Given the NBIS rating scale ranges from 0 to 9.
Then in the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.
So we know that p = 0.09.
Now, q = 1-p
q = 1-0.09
q = 0.91
Therefore, q = 0.91
Our goal is:
a). We need to find the probability that at least 3 will have an inspection rating of 4 or below in 2020.
b). Suppose that you actually observe 3 or more of the sample of 10 bridges with inspection rating of 4 or below in 2020, we need to know what inference we can make and why.