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

This problem in question follows binomial distribution, use following formula to calculate the probabilities:

P(x,r)=nCr(p)^r(q)^n-r, where, p is the probbaility of success, n is th etotal number of trials and r is the specific number of events.

a) P(x=0)=15C0(0.20)^0(0.80)^15=0.012

b) P(x=1)=15C1(0.20)^1(0.80)^14=0.058

c) P(x>7)=P(x=8)+P(x=9)+P(x=10)+P(x=11)+...+P(x=15)=0.0321

d) P(x=3)=15C3(0.20)^3(0.80)^12=0.205

e) P(x<5)=P(x=0)+P(x=1)+...+P(x=4)=0.630

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