Question

STATISTICS Quiz 4 1. Southern California Edison Co. has begun to promote ene discounted rates to consumers who k certain established eep their energy usage below ubsidy standards. A reduced their electricity cent report notes that 70% of Catalina Island residents have usage sufficiently to qualify for discounted rates. If 5 residential re su subscribers are randomly selected from Catalina Island a) find the probability ht al iv quall or the favorable ratos: (3 pts.) b) find the probability that at least four qualify for the favorable rates. (3 pts.) c) find the probability that most of the residents qualify for the favorable rates. 24,3 % (4 pt

Answer 1

Let X denotes the number of residential subscribers who qualify for the favorable rates among 5 randomly selected residential subscribers.

X ~ Binomial( n = 5, p = 0.7)

The probability mass function of X is

$P(X=x) = \binom{5}{x}*0.7^x*(1-0.7)^{5-x},x=0,1,2,3,4,5$

a) $P(X=5) = \binom{5}{5}*0.7^{5}*(1-0.7)^{5-5} = 0.7^5 = 0.16807$

b) $P(X \geq 4) = P(X=4) + P(X=5)$

$\Rightarrow P(X \geq 4) = \binom{5}{4}*0.7^{4}*(1-0.7)^{5-4} +\binom{5}{5}*0.7^{5}*(1-0.7)^{5-5}$

$\Rightarrow P(X \geq 4) = 0.36015 + 0.16807$

$\Rightarrow P(X \geq 4) = 0.528220$

c) Here,

Mean of X = E(X) = 5*0.7 = 3.5

P( most of the residents qualify for favorable rates) = P( X > = 3.5) $= P(X \geq 4) = 0.528220$