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 nothing. ?(Round to three decimal places as? needed.) b. What is the probability that all of the selected adults believe in? reincarnation? The probability that all of the selected adults believe in reincarnation is nothing. ?(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 nothing. ?(Round to three decimal places as? needed.) d. If 7 adults are randomly? selected, is 6 a significantly high number who believe in? reincarnation? A. No?, because the probability that 6 or more of the selected adults believe in reincarnation is less than 0.05. B. Yes?, because the probability that 6 or more of the selected adults believe in reincarnation is less than 0.05. C. Yes?, because the probability that 6 or more of the selected adults believe in reincarnation is greater than 0.05. D. No?, because the probability that 6 or more of the selected adults believe in reincarnation is greater than 0.05.

Explanation / Answer

p = 0.5

n = 7

it is a binomial distribution.

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

a) P(X = 6) = 7C6 * (0.5)^6 * (0.5)^1 = 0.055

b) P(X = 7) = 7C7 * (0.5)^7 * (0.5)^0 = 0.008

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

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

                  = 0.063

d) Option - C

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