According to a survey reported in the Business Week, 30% of adults in the U. S. said that the cell phone is the invention that they hate most but cannot live without. If a random sample of 6 adults in the U. S. is selected, find the probability that at least 3 in the sample hold this opinion. (a).1852 (b).0595 (c).0102 (d).0007 (e).2556

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Josue Rollins

Business

14 February, 14:47

According to a survey reported in the Business Week, 30% of adults in the U. S. said that the cell phone is the invention that they hate most but cannot live without. If a random sample of 6 adults in the U. S. is selected, find the probability that at least 3 in the sample hold this opinion. (a).1852 (b).0595 (c).0102 (d).0007 (e).2556

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Mouse · Answer 1

To calculate, the binomial distribution formula can be applied

P (X) = nCx * Px * (1 - P) ^ (n - x)

Random sample of 6 adults:

P (X≥3) = P (X=3) + P (X=4) + P (X=5) + P (X=6)

(6 C 3 ) 0.30^3 * 0.7 (6-3) + (6 C 4 ) 0.30^4 * 0.7^ (6-4) + (6 C 5 ) 0.30^5 * 0.7^ (6-5) + (6 C 6) 0.30^6 * 0.7^ (6-6) =

0.1852+0.0595+0.0102+0.0007

= 0.2556

[6 C 3 = 6! / (6-3) !3! = 1*2*3*4*5*6/1*2*3*1*2*3, and to calculate others apply to this formula]