Answer:
A. this is a binomial experiment because from a random sample of people the experiment consist in conduct a selected person based on what they think about the morals in USA (if this person agrees that moral values are lacking in USA or not). Considering a person agrees with this affirmation as a success, with probability of 0.45 and thinking about the opinion of those people as independent from each other. This is a binomial experiment.
B. P(x=15) = 0.05202 This is the probability that exactly 15 people think that moral values are lacking in USA
(This value is low considering that the 45% of the sample that agrees with the affirmation are 11 people, and we are asking that exactly 15 of the 25 agrees with it)
C. P(x≤10) = 0.24237 This is the probability that less than 10 people believe that moral values in USA are poor
Step-by-step explanation:
B. After affirm that this is a binomial experiment, we can find the probabilities that we need with formulas of a binomial experiment:
[tex]P(x=a) = {n\choose{a}}(0.45^{a})(0.55^{n-a})[/tex]
Where n is the number of objects in the sample, a the number of objects in the sample you want to give the probability and p is the probability of the event you consider success.
The probability of someone agreeing to the idea is 0.45 and the total of people in the sample are 25, so we find P(x=15)
[tex]P(x=15) = {25\choose{15}}(0.45^{15})(0.55^{10})[/tex]
P(x=15) = 0.05202
C. Now we need P(x<10), because x is a positive integer:
P(x<10) = P(x=0) + .... +P(x=9)
[tex]P(x<10)=\sum_{i=0}^{9}{P(x=i)}[/tex]
But we know the formula for P(x=i):
[tex]P(x<10)=\sum_{i=0}^{9}{{25\choose{i}}(0.44^{i})(0.55^{25-i})}[/tex]
And we just find those values (P(x=0), P(x=1), ..... P(x=9)) and we add them to get
P(x<10) = 0.24237
Answer:
Step-by-step explanation:
a) The experiment is a binomial experiment because of the following reasons
(i) Binomial experiment has a fixed number of trials, from the statement the experiment has a fixed number of trial, the trial is to check whether the overall state of moral value in the United State is poor or not and a fixed sample of 25 is being considered
(ii) In a binomial experiment, each trial is independent of one another
(iii) In a binomial experiment, there are only two possible outcomes, which are success or failure, yes or no, good or bad etc. from the statement the outcomes are poor or rich
(iv) The probability of each outcome remain constant throughout the experiment , from the experiment above, the probability of "poor" is 0.45 which is denoted p and that of "rich is 0.55 , which is denoted with q
(b) Using 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
Interpretation: The probability is low, it is not up to average, it means that the significance of the claim is not high
(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)
Interpretation: The probability is also low, it means the effect is not also high on the claim
