31. 42% of adults say cashews are their favorite kind of nut. You randomly selec

Question

31. 42% 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 probabilities.

(a) P(3) = ____ (Round to the nearest thousandth as needed.)

(b) P(x4) = ____ (Round to the nearest thousandth as needed.)

(c) P(x2) = ____ (Round to the nearest thousandth as needed.)

Explanation / Answer

PROBABILITY THAT CASHEWS IS FAVORITE = 0.42

PROBABILITY THAT CAASHEW IS NOT FAVORITE = 0.58

A) P(X= 3) = 12C3*(0.42)^3*(0.58)^9 = 0.121

B) P(X>=4) = 1 - [P(0)+P(1)+P(2)+P(3)

P(0)= 0.58^12 = 0.001

P(1) = 12C1*(0.42)^1*(0.58)^11 = 0.012

P(2) = 12C2*(0.42)^2*(0.58)^10 = 0.050

P(3) = 0.121

ADDING ALL WE WILL GET = 0.184

P(X>=4) = 1 - 0.184 = 0.816

C) P(X<=2) = P(0)+P(1)+P(2) [AS CALCULATED ABOVE)]

= 0.063

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