Using a survey conducted in Winter 2009, it was estimated that only 1% of New Zealanders have solar panels on their houses to generate electricity. Consider a random sample of 20 New Zealand households.
a) What is the probability that at least one of them has solar panels to generate electricity?
b) What is the probability that none of them have solar panels to generate electricity?
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Binomial Sampling Distribution:
P(n) = C(N,n) * p^n * (1-p)^(N-n)
where N = 20 and n = 0:
P(0) = C(20,0) * (1/100)^0 * (99/100)^(20-0) =
1 * 1 * 99^20 / 100^20 =
note: divided numerator and denominator by a common multiple of 10/
8179069375972306130 / 10000000000000000 =
P(0)= 0.8179
a) At least one has solar panels: P(n>0) = 1.0 – P(0) = 1.0 – 0.8179 = 0.1821
b) None of the 20 have solar panels: P(n=0) = P(0) = 0.8179