A Gallup poll reported in July 2014 the percentage of uninsured adults was 20%.

Question

A Gallup poll reported in July 2014 the percentage of uninsured adults was 20%. Let X denote the number of people with no health insurance. You randomly sample a group of 15 people. Find the following probabilities.

a) What is the probability that zero people in your sample do not have health insurance X=0

b) What is the probability that 1 person in your sample does not have health insurance X=1

c) What is the probability that more than 7 people in your sample do not have health insurance X>7

d) What is the probability that exactly 3 people in your sample do not have health insurance X=3

e). What is the probability that fewer than 5 people in your sample do not have health insurance X<5

Explanation / Answer

PROBABILITY OF NOT HAVING INSURANCE = 0.2

THEREFORE PROBABILITY OF HAVING THE INSURANCE = 0.8

NOW WE HAVE N = 15

A) P(X=0 INSURED) = 15C0*(0.2)^0*(0.8)^15 = 0.035

B) P(X = 1 INSURED) = 15C1*(0.2)^1*(0.8)^14 = 0.131

D) P(X=3) = 15C3*(0.2)^3*(0.8)^12 = 0.250

E) P(X<5) = P(0)+P(1)+P(2)+P(3)+P(4)

P(2) = 15C2*(0.2)^2*(0.8)^13 = 0.230

P(4) = 15C4*(0.2)^4*(0.8)^11 = 0.187

THEREFORE P(X<5) = 0.035+0.131+0.250+0.230+0.187 = 0.833

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