1 In Multnomah county, Oregon, only 27% of households have children aged 17 year

Question

1 In Multnomah county, Oregon, only 27% of households have children aged 17 years or younger.

Suppose eight households in Multnomah county are randomly selected to discuss educational support for K – 12. What is the probability that at least one household out of the eight selected will have children aged 17 years of age or younger.

2 In Washington county, Oregon, 36% of households have children aged 17 years or younger.

Suppose four households in Washington county are randomly selected to discuss educational support for K – 12. What is the probability that exactly four households out of the four selected will have children aged 17 years of age or younger.

Explanation / Answer

1) Number of households selected i.e. n = 8

Proportion of children aged 17 years or younger = 0.27 i.e. p

Let X be the number of children aged 17 years of age or younger ( X follows binomial with n= 8 and p = 0.27)

P(X>=1) = 1 - P(X<1) = 1- P (X=0)

= 1 - (8C0 (0.27)0 (1-0.27)8-0 ) = 0.9194

2) Number of households selected i.e. n = 4

Proportion of children aged 17 years or younger = 0.36 i.e. p

Let X be the number of children aged 17 years of age or younger ( X follows binomial with n= 4 and p = 0.36)

P(X=4) = 4C4 (0.36)4 (1-0.36)4-4 = 0.0168

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