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. PLEASE ANSWER QUESTIONS A through E.

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 follows binomial distribution. Use the following formula.

P(x,r,p)=nCr(p)^r(q)^n-r, where, p denotes probbaility of success, r denotes the specific number of events to have occurred and n denotes the total number of trials.

a) P(X=0)=15C0(0.15)^0(0.85)15=0.087

b) P(X=1)=15C1(0.15)^1(0.85)^14=0.231

c) P(X>7)=P(X=8)+P(X=9)+...+P(X=15)=0.0006

d) P(X=3)=15C3(0.150^3(0.85)^12=0.218

e) P(X<5)=P(X=0)+P(X=1)+...+P(X=4)=0.938

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.