According to a publication of the Centers for Disease Control and Prevention, 16

Question

According to a publication of the Centers for Disease Control and Prevention, 16.5% of people under age 65 have no health insurance coverage. If 15 people under the age of 65 are randomly selected, let X represent the number who have no health insurance coverage. Find the probability that all 15 have health insurance coverage. Use correct probability notation and round to four decimal places. Find the probability that fewer than 6 do not have health insurance coverage. Use correct probability notation and round to four decimal places.

Explanation / Answer

a).

n=15

P=0.165

Binomial distribution used.

P(X=x) = (nCx) px (1-p)n-

P(X=15) = (15C15) 0.16515 (1-0.165)15-15

P(X = 15) = 0.000000000002

b).

P( x <6) = P( x=0)+P( x=1)+P( x=2)+P( x=3)+P(x=4)+P( x=5)

X

P(X)

0

0.0669

1

0.1982

2

0.2742

3

0.2348

4

0.1392

5

0.0605

P( x<6) =0.9738

X

P(X)

0

0.0669

1

0.1982

2

0.2742

3

0.2348

4

0.1392

5

0.0605

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