1) A four-year study of bottled water brands conducted by Natural resources defe

Question

1) A four-year study of bottled water brands conducted by Natural resources defense council found that 80% of bottled water is just tap water packaged in a bottle. In a sample of 10 bottled water brands, let X equal the number of these brands that use tap water a) Find the probability that at least one bottle is tap water. b) Find the probability that exactly five of the bottles are just tap water. c) Find the mean and standard deviation of the number of bottles that are tap water d) Find the one standard deviation interval probability e) Find P(X>7| Xs9).

Explanation / Answer

a)

P(X>=1) = 1 - P(X<1)

= 1 - P(X=0)

= 1 - 10C0 * 0.8^0 * 0.2^10

= 0.9999

b)

P(X=5) = 10C5 * 0.8^5 * 0.2^5

= 0.0264

c)

mean = np = 10 * 0.8 = 8

standard deviation = sqrt(10 * 0.8 * 0.2) = 1.2649

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