Question

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

Answer 1

Answer:

Explanation:

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]