Question 978976: 31% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient use technology to find the probabilities.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! p = 0.31
n = 12
I'm going to use a TI-84 calculator. Specifically, I'm using the binompdf and binomcdf functions.
(a)
Exactly 3
P(x = k) = binompdf(n,p,k) = binompdf(12, 0.31, 3) = 0.23235
P(x = 3) = 0.23235
Answer: 0.23235
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(b)
At least 4
P(x <= k) = binomcdf(n, p, k) = binomcdf(12, 0.31, 3) = 0.46194
P(x <= 3) = 0.46194
P(x >= 4) = 1 - P(x < 4)
P(x >= 4) = 1 - P(x <= 3)
P(x >= 4) = 1 - 0.46194
P(x >= 4) = 0.53806
Answer: 0.53806
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(c)
At most two
P(x <= k) = binomcdf(n, p, k) = binomcdf(12, 0.31, 2) = 0.22959
P(x <= 2) = 0.22959
Answer: 0.22959
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