Over the past 50 years, one-half of all cities that apply have received mass tra
ID: 3361909 • Letter: O
Question
Over the past 50 years, one-half of all cities that apply have received mass transportation grants from the federal government. In the last round of grants, eight southern cities applied but none received a grant. Assume that all cities were equally qualified to receive the grants. What is the probability that no southern city receives a grant? The Southern Governors' Association is considering bringing a lawsuit against the federal government for discrimination in the awarding of the transporta- tion grants. Do you think that the Southern Governors' Association would have a strong case or a weak case? How would you advise the association to proceed?Explanation / Answer
We use the binomial distribution if the following requires four assumptions are satisfied:
1) sample size (n) is fixed here n = 8 so this assumption satisfy
2) Each replication of the process results in one of two possible outcomes (success or failure),
Here success is "cities received mass transportation grants from the federal government", and failure is " "cities does not received mass transportation grants from the federal government".
3)The probability of success is the same that is constant for each replication.
Here proportion of "cities received mass transportation grants from the federal government" is half = 0.5
4) The replications(that is trials) are independent,
All the four assumptions of binomial distribution are satisfied so we can used it to find the probability.
Probability of all the cities are not selected = P(X = 0) = 0.5^8 = 0.003906
which is very small (< 0.05) so the events "all of the 8 cities are not selected" is an unusual event.
Therefore the Southern Governors' Association would have a strong case .
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