SOLUTION: 60% of adults say that cashews are their favorite nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cash

Algebra ->  Probability-and-statistics -> SOLUTION: 60% of adults say that cashews are their favorite nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cash      Log On


   

Question 767873: 60% of adults say that cashews are their favorite nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly 3, (b) at least 4, and (c) at most two. If convenient, use technology to find the probabilities... (a)P(3)=
Round to the nearest thousandth as needed.
I really need some help with these questions. I figured out all the rest of them, but these are really hard to understand. Whomever helps me I would be so thankful for this help.
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
60% of adults say that cashews are their favorite nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is
X~Binomial(12,0.6)
(a) exactly 3
P%28X+=+3%29+=+%28matrix%282%2C1%2C12%2C3%29%29%280.6%5E3%29%280.4%5E7%29 = highlight%280.012%29
(b) at least 4
P(X ≥ 4) = sum%28%28matrix%282%2C1%2C12%2Cx%29%29%280.6%5Ex%29%280.4%5E%2812-x%29%29%2Cx+=+4%2C12%29 = highlight%280.985%29
and (c) at most two.
P(X ≤ 2) = sum%28%28matrix%282%2C1%2C12%2Cx%29%29%280.6%5Ex%29%280.4%5E%2812-x%29%29%2Cx+=+0%2C2%29 = highlight%280.003%29
Round to the nearest thousandth as needed.