Question

Based on a​ poll,

50%

of adults believe in reincarnation. Assume that

6

adults are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.

A.What is the probability that exactly 5 of the selected adults believe in​ reincarnation?

The probability that exactly 5 of the 6 adults believe in reincarnation is

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

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

C. What is the probability that at least 5 of the selected adults believe in​ reincarnation?

The probability that at least 5 of the selected adults believe in reincarnation is

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

D.If 6 adults are randomly​ selected, is 5 a significantly high number who believe in​ reincarnation?

​

Answer 1

a)

Here, n = 6, p = 0.5, (1 - p) = 0.5 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 5)
P(X = 5) = 6C5 * 0.5^5 * 0.5^1
P(X = 5) = 0.0938

b)

Here, n = 6, p = 0.5, (1 - p) = 0.5 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 6)
P(X = 6) = 6C6 * 0.5^6 * 0.5^0
P(X = 6) = 0.0156

c)

Here, n = 6, p = 0.5, (1 - p) = 0.5 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 5).
P(X >= 5) = (6C5 * 0.5^5 * 0.5^1) + (6C6 * 0.5^6 * 0.5^0)
P(X >= 5) = 0.0938 + 0.0156
P(X >= 5) = 0.1094

d)

No,because probability is higher tahn 0.05 i.e 0.0938