Answer:
This is an incomplete question. I will need to add the missing piece of information for us to begin.
In a recent poll, the Gallup organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 25 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Answer the questions below, showing work. Bare answers are not acceptable. (Showing work means writing the calculator command you used with correct input values in the correct order.)
a) Explain why this is a binomial experiment.
b) Find and interpret the probability that exactly 15 of those surveyed felt the overall state of moral values in the United States is poor.
c) Find and interpret the probability that no more than 10 of those surveyed felt the overall state of moral values in the United States is poor.
Answer:
Let's take it one at A time.
a) The experiment is a binomial experiment due to the fact that:
(i) Binomial experiment has a specified amount of trials, from the question we see a specified amount of trial which is used to view if the whole amount of moral value in the United State is poor or not and a specified amount of 25 is given.
(ii) In a binomial experiment, a trial is not depending on the outcome of another
(iii) In a binomial experiment, we see mainly two likely occurrences, it can be success or failure, yes or no, good or bad etc. from the question the occurrence is poor or rich
(iv) The likelihood of each occurrences does not change in the course of the experiment, in the question, the percent likelihood of "poor" is 0.45 which is noted by p and q for "rich" is 0.55.
(b) Recalling the binomial distribution formula:
N = 25,
p = 0.45,
q = 0.55
P ( X = r ) = n∁r p^ r q^ (n - r)
P ( X = 15 ) = 25∁15 {( 0.45 )} ^15 { ( 0.55 )}^10
P ( X = 15 )
= 3268760 × 0.0000062833 × 0.00253295162
P ( X = 15 ) = 0.052
Feedback:
The percent likelihood is low, it doesn't measure up to average, it implies that the significance of the claim is not high, that is to say it's low.
(c) The probability of no more than 10 implies
P ( X ≤ 10 )
P ( X ≤ 10 )
= P ( X = 0 ) + P ( X =1 )+ P ( X = 2 ) + ⋯ + P ( X = 10 )
= 0.0000003229 + 0.00000660476 + 0.00006484674 + 0.00040676591 + 0.00183044658 + 0.00629008008 + 0.01715476386 + 0.03809694312 + 0.07013300892 + 0.10838737742 + 0.14188893044
P ( = 0.38 )
Feedback:
The percent likelihood is quite low too, it implies a low effect on the claim
