Statistic question?

14. The Board of Realtors of a small city reports that 80% of the houses that are sold have


been on the market for more than 6 months. The Board takes a random sample of 15


homes that have recently been sold and counts the number that were on the market for


more than 6 months. What is the Probability that of 15 homes in the sample:





a. less than 12 have been on the market for more than 6 months?


b. between 8 and 13 have been on the market for more than 6 months?


c. at least 10 homes have been on the market for more than 6 months?


d. at most 4 have been on the market for more than 6 months?

Statistic question?
Binomial distribution problem. For each part, some things don't change. They are n = 15, p = 80% = 0.8, q = 20% = 0.2


The only thing that _will_ change is x.





a. less than 12 means x = 0, 1, 2, 3, 4, ... 11. So, you'd have to find the probability of each value and add them all...which sucks. To simplify this a bit, use the idea of complements:


P(A') = 1 - P(A). With this you can say:


P(0...11) = 1 - P(12..15)


You'd still have to find the probability of 12, 13, 14, and 15, but that's less work than 0 through 11.


The way around _this_ is to use the table in your book which gives the probability for some standard sample sizes (n = 15 being one of them) and find the probability of 12 - 15 using the table and add those together, then subtract it from 1.





b. between 8 and 13 = P(8, 9, 10, 11, 12, 13)





c. at least 10 = P(10, 11, 12, 13, 14, 15)





d. at most 4 = P(0, 1, 2, 3, 4)





You should have a table in your book, if not, then use the formula,


P(x) = (x n)*p^x*q^(n-x) for each number needed in each part.


Hope this helps.

apricot