11.9% of the population is 65 or older. Find the probability that the following

Question

11.9% of the population is 65 or older. Find the probability that the following number of persons selected at random from 20 people are 65 or older. The probability that at least 3 are 65 or older is _____? (round to 3 decimal places )

A study determined that 4% of children under 18 years of age live with their father only. Find the probability that at tleast 3 persons selected at random from 12 children under 18 years of age lived with their father only.The probability that at tleast 3 children live with their father only is _______?(Do not round until the final answer. Then round to the nearest thousandth as needed.)

Explanation / Answer

X ~ Binomial(n,p)

Binomial probability distribution is

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

a)

n = 20, p = 0.119

P(X >= 3) = 1 - P( X <= 2)

= 1 - { P( X = 0) + P( X = 1) + P X( X = 2) }

= 1 - { 20C0 0.1190 0.88120 + 20C1 0.1191 0.88119 + 20C2 0.1192 0.88118 }

= 1 - 0.568744

= 0.431

b)

n = 12 , p = 0.04

P(X >= 3) = 1 - P( X <= 2)

= 1 - { P( X = 0) + P( X = 1) + P X( X = 2) }

= 1 - { 12C0 0.040 0.9612 + 12C1 0.041 0.9611 + 12C2 0.042 0.9610 }

= 1 - 0.989271

= 0.011

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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