SOLUTION: 38% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say c

Question 1011230: 38% of adults say cashews are their favorite kind of 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 three, (b) at least four, and (c) at most two. If convenient, use technology to find the possibilities.
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Exactly 3
12C3*(.38^3)*(.62^9)=0.1634 ANSWER TO A
Exactly 2=12C2(0.38^2)(0.62^10)=0.0800
Exactly 1=12*0.38*0.62^11=0.0237
0=0.62^12=0.0032
At least 4 is 1-the probability of 0,1,2,3=1-0.2703=0..7297
at most 2 is P(2,1,0)=0.1069.
As a side note the expected value if 12*0.38=4.56, so 4 and 5 will be a large portion of the probability. This serves as a check for "at least 4".

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
38% of adults say cashews are their favorite kind of 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) P(exactly three) = 12C3(0.38)^3*(0.62)^9 = binompdf(12,0.38,3) = 0.1634
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(b) P(at least four) = 1 - binomcdf(12,0.38,3) = 0.7296
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(c) P(at most two) = binomcdf(12,0.38,2) = 0.1069
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Cheers,
Stan H.
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