Question

Montana is working on budgeting money for primary state highway repairs for the next fiscal year. Previous research conducted on the U.S.’s infrastructure indicates that thirty percent of roads need major repairs. Suppose when considering a roadway for repair, they consider the entire length of road and ultimately classify each roadway as “needing repairs” or “not.” Let X be the number of primary state highways (of which there are forty-nine) that need repairs, and assume that each highway’s need is independent of any other highway.

(a) [2 pts] Describe the distribution of X, indicating any parameter values necessary in proper notation.

(b) [3 pts] Find the expected value and variance of X.

(c) [2 pts] Calculate the probability that ten primary highways need repairs.

(d) [2 pts] What is the probability that more than twenty-two state highways need repairs?

(e) [4 pts] What distribution will the sample proportion of primary roads that need repairs follow if we randomly sample thirty-five roads? Specify the parameters for this distribution, check any conditions necessary, and explain why pˆ follows this distribution.

(f) [2 pts] What is the probability of observing ten highways in a sample of thirty-five that need repairs?

(g) [2 pts] What is the probability of observing twenty-two or more highways that need repairs in a sample of thirty-five?

Answer 1

kennd dga frven.pren'ơm.ndn *r.ne< d X be the numbe. 억 1mm d he lb -=49 (O - I4.7 O.29 3a1 3 0:44 136 4-149 823 о-о 920 49-γ