7. (4 marks) Suppose that 70% of the voting population in a large Canadian city is in favour of permitting construction of a Level IV virus laboratory in the inner city. The city is contemplating having a referendum on the issue. A random sample of four eligible voters is interviewed. Among those persons to be interviewed:
What is the probability that at least three people favour allowing construction?
What is the expected number of persons in favour of allowing construction?
What is the variance of the number of persons in favour of allowing construction?
Here, n = 4, p = 0.7, (1 - p) = 0.3 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 -
p)^(n - x)
We need to calculate P(X >= 3).
P(X >= 3) = (4C3 * 0.7^3 * 0.3^1) + (4C4 * 0.7^4 * 0.3^0)
P(X >= 3) = 0.4116 + 0.2401
P(X >= 3) = 0.6517
mean = np = 4 * 0.70 = 2.8
variance = npq
= 4 * 0.70 *(1-0.70)
= 0.8400
7. (4 marks) Suppose that 70% of the voting population in a large Canadian city is...
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