(a) The probability can be found by using binomial distribution:

P(x >=12) = sum_{k = 12}^20 (20 C k) 0.6^k * 0.4^{20-k}, wher 20 C k = 20!/(k! * (20 - k)!) is the binomial coefficient.

It is also possible to use the technology. For example, use DISTR menu on TI-83 Plus,

choosing binomcdf(20, 0.6, 11) = 0.404 and P(x >= 12) = 1 - 0.404 = 0.596

Answer: 0.596

(b) P(x < = 6) = binomcdf(20. 0.6, 6) = 0.006

(c) The expected value for the binomial distribution is 20 * 0.6 = 12

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