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:
, n= sample size.
a.
![P(X=5) = ^5C_5(0.20)^5(1-0.20)^{5-5}=(1)(0.20)^5(1)\\\\=0.00032](https://tex.z-dn.net/?f=P%28X%3D5%29%20%3D%20%5E5C_5%280.20%29%5E5%281-0.20%29%5E%7B5-5%7D%3D%281%29%280.20%29%5E5%281%29%5C%5C%5C%5C%3D0.00032)
b. ![P(X\geq4)=P(4)+P(5)](https://tex.z-dn.net/?f=P%28X%5Cgeq4%29%3DP%284%29%2BP%285%29)
![^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](https://tex.z-dn.net/?f=%5E5C_4%280.20%29%5E4%281-0.20%29%5E%7B5-4%7D%2B0.00032%5C%5C%5C%5C%3D%285%29%280.20%29%5E4%280.80%29%2B0.00032%5C%5C%5C%5C%3D0.0064%2B0.00032%5C%5C%5C%5C%3D0.00672)