Question 474197: 33% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite. F ind the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most tow. If convenient use technology to find the probabilities.
(a) P(3)= round to the nearest thousandth as needed
(b) P(x>_4)= round to the nearest thousandth as needed.
(c) P(x_<2) = round to the nearest thousandth as needed.
Thank you.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The probability of  successes in  trials where  is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where ) is the number of combinations of things taken at a time and is calculated by !}) , and which can be calculated in MS Excel using:
=COMBIN(n,k)
Part a)
Hence:
\ =\ \left(12\cr\ 3\right\)\left(0.33\right)^3\left(0.67\right)^{9})
Which can be calculated using Excel:
=BINOMDIST(3, 12, 0.33, FALSE)
Part b)
Hence:
\ =\ \sum_{i\,=\,4}^{12}\ \left(12\cr\ i\right\)\left(0.33\right)^i\left(0.67\right)^{12\,-\,i})
But this is equal to:
\ =\ 1\ -\ \sum_{i\,=\,0}^3\ \left(12\cr\ i\right\)\left(0.33\right)^i\left(0.67\right)^{12\,-\,i})
Which can be calculated using Excel:
=1 - BINOMDIST(3, 12, 0.33, TRUE)
Part c)
Hence:
\ =\ \sum_{i\,=\,0}^2\ \left(12\cr\ i\right\)\left(0.33\right)^i\left(0.67\right)^{12\,-\,i})
Which can be calculated using Excel:
=BINOMDIST(2, 12, 0.33, TRUE)
John
My calculator said it, I believe it, that settles it
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