Based on a? poll, 50?% of adults believe in reincarnation. Assume that 7 adults

Question

Based on a? poll, 50?% of adults believe in reincarnation. Assume that 7 adults are randomly? selected, and find the indicated probability. Complete parts? (a) through? (d) below.

a. What is the probability that exactly

6 of the selected adults believe in? reincarnation? The probability that exactly 6 of the 7

adults believe in reincarnation is

?(Round to three decimal places as? needed.)

b. What is the probability that all of the selected adults believe in? reincarnation?

?(Round to three decimal places as? needed.)

c. What is the probability that at least

6

of the selected adults believe in? reincarnation?The probability that at least

6 of the selected adults believe in reincarnation is

?(Round to three decimal places as? needed.)

Explanation / Answer

It is a binomial distribution.

n = 7

p = 0.5

P(X = x) = nCx * px * (1 - p)n - x

a) P(X = 6) = 7C6 * (0.5)^6 * (0.5)^1 = 0.0547

b) P(X = 7) = 7C7 * (0.5)^7 * (0.5)^0 = 0.0078

c) P(X > 6) = P(X = 6) + P(X = 7)

                 = 7C6 * (0.5)^6 * (0.5)^1 + 7C7 * (0.5)^7 * (0.5)^0

                = 0.0625

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