SOLUTION: *****Of all the trees planted by a landscaping firm, 55% survive. What is the probability that 12 or more of the 14 trees they just planted will survive? (Use a table of binomi

Question 965490: *****Of all the trees planted by a landscaping firm, 55% survive. What is the probability that 12 or more of the 14 trees they just planted will survive?
(Use a table of binomial probabilities. Give your answer correct to four decimal places.)
I have been stuck on this for days!! Please help me. If possible please show step-by-step instructions.
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
55% survive, so p = .55
this means that 45% don't survive.
q = 1 - p = 1 - .55 = .45

you have p = .55
you have q = .45

the binomial probability formula is:

p(x) = c(n,x) * p^x * q^(n-x)

x represents the ratio of plants that survive.
n is the total number of trees that were planted.
p(x) is the probability that x will survive.
c(n,x) is the number of possible combinations of n plants taken x at a time where order is not important.
c(n,x) is defined as n! / (x! * (n-x)!)

you want to know the probability that 12 or more will survice.

this is equal to the probability that exactly 12 will survive plus the probability that exactly 13 will survice plus the probability that exactly 14 will survive.

so you need to find p(12) + p(13) + p(14).

p(12) = c(14,12) * p^12 * q^2 = 91 * .55^12 * .45^2 = .0141194797

p(13) = c(14,13) * p^13 * q^1 = 14 * .55^13 * .45^1 = .0026549449

p(14) = c(14,14) * p^14 * q^0 = 1 * .55^14 * .45^0 = .0002317809043

p(12) + p(13) + p(14) = .0170062055

that's your solution.

here's one of the combination calculations to show you how they're done.

c(14,12) = 14! / (12! * 2!) = (14 * 13 * 12!) / (12! * 2!) = (14 * 13) / 2! = 7 * 13 = 91.

RELATED QUESTIONS
Of all the trees planted by a landscaping firm, 70% survive. What is the probability that (answered by Fombitz)

Of all the trees planted by a landscaping firm, 70% survive. What is the probability that (answered by ewatrrr)

Of all the trees planted by a landscaping firm, 35% survive. What is the probability that (answered by stanbon)

Of all the trees planted by a landscaping firm, 75% survive. What is the probability that (answered by Fombitz)

Ninety percent of the trees planted by a landscaping firm survive. What is the... (answered by solver91311)

2.Ninety percent of the trees planted by a landscape firm survive. If 20 trees are... (answered by ikleyn)

Eighty percent of trees planted by a woodlands conservation group survive. What is the... (answered by ewatrrr)

Trees planted by a landscaping firm have a 90% one-year survival rate. If they plant 12... (answered by Boreal)

Trees planted by a landscaping firm have a 95 % one-year survival rate, If they plant 12 (answered by ikleyn)