Question

A national standard requires that public bridges over 20 feet in length must be inspected and rated every 2 years. The rating scale ranges from 0​ (poorest rating) to 9​ (highest rating). A group of engineers used a probabilistic model to forecast the inspection ratings of all major bridges in a city. For the year​ 2020, the engineers forecast that 4​%of all major bridges in that city will have ratings of 4 or below. Complete parts a and b.

a. Use the forecast to find the probability that in a random sample of 10 major bridges in the​ city, at least 3 will have an inspection rating of 4 or below in 2020.

​P(x≥​3)=________________ ​(Round to five decimal places as​ needed.)

Answer 1

Solution:-

a) The probability that in a random sample of 10 major bridges in the​ city, at least 3 will have an inspection rating of 4 or below in 2020 is 0.00621.

p = 0.04

n = 10

x = 3

By applying binomial distribution:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 3) = 1 - P(x = 0) + P(x = 1) + P(x = 2)

P(x > 3) = 1 - 0.664832 - 0.277014 + 0.051940

P(x > 3) = 1 - 0.993786

P(x > 3) = 0.00621