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 30 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. Use the Tech Help button for further assistance.

(a) Find and interpret the probability that exactly 18 of those surveyed feel the state of morals is poor.

The probability that exactly 18 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.

A. In 100 trials of this experiment, we expect about 8 to result in exactly 18 adults who feel the state of morals is poor.

B. In 100 trials of this experiment, we expect about 15 to result in exactly 18 adults who feel the state of morals is poor.

C. In 100 trials of this experiment, we expect about 19 to result in exactly 18 adults who feel the state of morals is poor.

D. In 100 trials of this experiment, we expect about 13 to result in exactly 18 adults who feel the state of morals is poor.

(b) Find and interpret the probability that no more than 14 of those surveyed feel that state of morals is poor. The probability that no more than 14 of those surveyed feel that state of morals is poor is ____. (Round to four decimal places as needed.)

Interpret the results. Choose the correct answer below.

A. In 100 trials of this experiment, we expect about 28 to result in no more than 14 adults who feel the state of morals is poor.

B. In 100 trials of this experiment, we expect about 1 to result in no more than 14 adults who feel the state of morals is poor.

C. In 100 trials of this experiment, we expect about 8 to result in no more than 14 adults who feel the state of morals is poor.

D. In 100 trials of this experiment, we expect about 43 to result in no more than 14 adults who feel the state of morals is poor.

Answer 1

p = 0.5

n = 30

a) P(X = 18) = 30C18 * 0.5¹⁸ * (1 - 0.5)^30-18 = 0.0806

Option-A) In 100 trials of this experiment, we expect about 8 to result in exactly 18 adults who feel the state of morals is poor.

b) P(X < 14) = P(X = 0) + P(X = 1) + ... + P(X = 14)

                    = 30C0 * 0.5⁰ * 0.5³⁰ + 30C1 * 0.5¹ * 0.5²⁹ + ... + 30C14 * 0.5¹⁴ * 0.5¹⁶

                    = 0.4278

Option-D) In 100 trials of this experiment, we expect about 43 to result in no more than 14 adults who feel the state of morals is poor.