Frogs. A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had establishedthat this trait is...

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in
Let X denote number of frogs with trait in n = 12 independent frogs, where
each has a probability p = 0.125
We denote this by:
X ∼ Binomial(n = 12, p = 0.125)
A P (X = 0), n = 12, p = 0.125
X ∼ Binomial(n = 12, p = 0.125)
P (X = 0) =
(
n
x
)
px(1−p)n−x =
(12
0
)
(0.125)0(1−0.125)12−0 = 1∗(0.125)0(0.875)12 =
0.201417 ≈ 0.201417 ≈ 0.201
P (X = 0) = 0.201
Using excel function BinomDist(0,12,0.125,false) or TI-83/84 function
binompdf(12,0.125,0), exact answer is 0.201417238
B P (X ≥ 2), n = 12, p = 0.125
P (X ≥ 2) = 1 − P (X < 2)
We first calculate:
P (X < 2) = P (0 ≤ X < 2) = P (0 ≤ X ≤ 1) = P (X = 0, 1)
= P (X = 0) + P (X = 1) (because these are disjoint events)
P (X = 0) =
(12
0
)
(0.125)0(1 − 0.125)12 = 1(0.125)0(0.875)12 ≈ 0.201417
P (X = 1) =
(12
1
)
(0.125)1(1 −...