Question

Suppose that a recent poll found that 50% of adults in a certain country believe that the overall state of moral values is poor. If a survey of a random sample of 20 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through (e) below. Click here to view the table for the binomial probability distribution. Click here to view the table for the cumulative binomial probability distribution. (a) Find and interpret the probability that exactly 12 of those surveyed feel the state of morals is poor. . The probability that exactly 12 of those surveyed feel the state of morals is poor is (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. In 100 trials of this experiment, we expect about v to result in exactly 12 adults who feel the state of morals is poor.

Answer 1

given is binomial probability distribution

the probability of a binomial function for P(X = x) = ⁿC_xp^x(1-p)^n-x

n = number of trails = 20

x = number of events.

probability of success p = 0.5

a) P(X = 12) = ²⁰C₁₂*0.5¹²*0.5⁸ = 0.1201

interpretation

In 100 trails of this experiment we expect about 12 to result in 12 adults who feel the state of morals is poor.

b) P(X<=8) = sum of P(X=xi) for i = 1 to 8

P(X<=8) = 0.2517

In 100 trails of this experiment we expect about 25 to result in no more than 8 adults who feel the state of morals is poor.

c) P(X>13) = 0.0577

In 100 trails of this experiment we expect about 5.77 to result in more than 13 adults who feel the state of morals is poor.

d) P(X=10) + P(X=11) = 0.3364

In 100 trails of this experiment we expect about 33.64 to result in 10 or 11 adults who feel the state of morals is poor.

e) P(X>=18) = P(X=18) + P(X=19) + P(X=20) = 0.0002

Yes it is unusual because the probability is very less.