According to government data, the probability that an adult was never in a museu

Question

According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fewer were never in a museum? o 0.002 o0.200 e 0820 Question 2 2 pts Provide an appropriate response. A recent article in the paper claims that government ethics are at an all-time low. Reporting on a recent sample, the paper claims that 41% of all constituents believe their representative possesses low ethical standards. Suppose 20 of a representative's constituents are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 constituents sampled bel lieve their representative possesses low ethical standards. 0593087 :0.596302 0 0.372646 0.245893

Explanation / Answer

For binomial distribution, P(X) = nCx px qn-x

1) n = 10

p = 0.15

q = 1 - p = 0.85

P(2 or fewer have never visited a museum) = P(0) + P(1) + P(2)

= 0.8510 + 10x0.15x0.859 + 10C2 x 0.152 x 0.858

= 0.1969 + 0.3474 + 0.2759

= 0.820

2) n = 20

p = 0.41

q = 0.59

P(more than 8 and fewer than 12) = P(9) + P(10) + P(11)

= 20C9x0.419x0.5911 + 20C10x0.4110x0.5910 + 20C11x0.4111x0.599

= 0.1658 + 0.1268 + 0.0801

= 0.3727

(Third option - 0.372646)

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