Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below certain established subsidy standards. A recent report notes that 20% of island residents of a country have reduced their electricity usage sufficiently to qualify for discounted rates. If five residential subscribers are randomly selected from a city on this island find the probability of each of the following events.

a. All five qualify for the favorable rate
b. At least four qualify for the favorable rates

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JeanaShupp JeanaShupp · Answer 1 · 2020-10-14T03:14:24+02:00

Answer: a. 0.00032 B. 0.00672

Step-by-step explanation:

Given: Proportion of island residents of a country have reduced their electricity usage (p) = 20%= 0.20

Here, residents have two choices either reduced electricity usage or not , hence it follows binomial distribution

Let X be a binomial variable that represents the number of successes .

Binomial distribution formula:

[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex], n= sample size.

a.

[tex]P(X=5) = ^5C_5(0.20)^5(1-0.20)^{5-5}=(1)(0.20)^5(1)\\\\=0.00032[/tex]

b. [tex]P(X\geq4)=P(4)+P(5)[/tex]

[tex]^5C_4(0.20)^4(1-0.20)^{5-4}+0.00032\\\\=(5)(0.20)^4(0.80)+0.00032\\\\=0.0064+0.00032\\\\=0.00672[/tex]