Suppose that a recent poll found that 55% of adults in a certain country believe

Question

Suppose that a recent poll found that 55% 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 conducted in which they are asked to disclose their feeling 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 21 of those surveyed feel the state of morals is poor. The probability that exactly 21 of those surveyed feel the state of morals is poor is .0382. (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 4 to result in exactly 21 adults who feel the state of morals is poor. B. In 100 trials of this experiment, we expect about 9 to result in exactly 21 adults who feel the state of morals is poor. C. In 100 trials of this experiment, we expect about 11 to result in exactly 21 adults who feel the state of morals is poor. D. In 100 trials of this experiment, we expect about 15 to result in exactly 21 adults who feel the state of morals is poor. (b) Find and interpret the probability that no more than 15 of those surveyed feel that state of is poor. The probability that no more than 15 of those surveyed feel that state of is poor is (Round to four decimal places as needed.)

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 15) = P(X=14) + P(X=13) + P(X=12) + P(X=11) + P(X=10) + P(X=9) + P(X=8) + P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 30 14 ) * 0.55^14 * ( 1- 0.55 ) ^16 + ( 30 13 ) * 0.55^13 * ( 1- 0.55 ) ^17 + ( 30 12 ) * 0.55^12 * ( 1- 0.55 ) ^18 + ( 30 11 ) * 0.55^11 * ( 1- 0.55 ) ^19 + ( 30 10 ) * 0.55^10 * ( 1- 0.55 ) ^20 + ( 30 9 ) * 0.55^9 * ( 1- 0.55 ) ^21 + ( 30 8 ) * 0.55^8 * ( 1- 0.55 ) ^22 + ( 30 7 ) * 0.55^7 * ( 1- 0.55 ) ^23 + ( 30 6 ) * 0.55^6 * ( 1- 0.55 ) ^24 + ( 30 5 ) * 0.55^5 * ( 1- 0.55 ) ^25 + ( 30 4 ) * 0.55^4 * ( 1- 0.55 ) ^26 + ( 30 3 ) * 0.55^3 * ( 1- 0.55 ) ^27 + ( 30 2 ) * 0.55^2 * ( 1- 0.55 ) ^28 + ( 30 1 ) * 0.55^1 * ( 1- 0.55 ) ^29 + ( 30 0 ) * 0.55^0 * ( 1- 0.55 ) ^30
= 0.2309

P( X > = 15 ) = 1 - P( X < 15) = 0.7691

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