Question 978976
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: <font color="red">0.23235</font>


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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: <font color="red">0.53806</font>

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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: <font color="red">0.22959</font>