Respuesta :
Answer:
a) μ = 41, σ = 4.9; b) For every 100 adults, the mean is the number of them that would be expected to believe the overall state of moral values is poor; c) No, it would not.
Step-by-step explanation:
This is a binomial distribution. This is because 1) there is a fixed number of trials (100); 2) there are two outcomes (either they do feel it's poor or they don't feel it's poor); 3) each trial is independent of each other; 4) the probability of success is the same for each trial.
a) Since this is a binomial distribution, the mean is given by μ = np, where n is the number of trials and p is the probability of success. This gives us
μ = 100(0.41) = 41
The standard deviation is given by
σ = √(npq), where n is the number of trials, p is the probability of success and q is the probability of failure. Since p = 0.41, this makes q = 1-0.41 = 0.59; this gives us
σ = √(100(0.41)(0.59)) = √(24.19) ≈ 4.9
b) The mean tells us the average number of people out of the sample that feel the state of moral values is poor.
c) A data value that is unusual is one that is more than 2 standard deviations from the mean. In this case, the number in question is the mean; this means it is 0 standard deviations from the mean, so it is not an unusual value.
Using the binomial distribution, we have that:
a) The mean is of 41, with a standard deviation of 4.92.
b)
The correct option is:
B. For every 100 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor.
c) It would not be unusual, as it is within 2 standard deviations of the mean.
For each adult, there are only two possible outcomes. Either they believe the overall state of morals is poor, or they do not. The belief of an adult is independent of any other adult, which means that the binomial distribution is used to solve this question.
The binomial probability distribution gives the probability of x successes on n trials, with p being the probability of a success in a single trial.
- The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
- The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
- A value of X is said to be unusual if it is more than 2.5 standard deviations from the mean.
In this problem:
- 100 adults, thus [tex]n = 100[/tex]
- 41% believe that the overall state of morals is poor, thus [tex]p = 0.41[/tex].
Item a:
The mean is:
[tex]E(X) = np = 100(0.41) = 41[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.41)(0.59)} = 4.92[/tex]
The mean is of 41, with a standard deviation of 4.92.
Item b:
- The mean is the expected value of the number of adults that believe the morals are poor, out of the 100 sampled, thus, option b is correct.
Item c:
41 is the mean, so it would not be unusual, as it is within 2 standard deviations of the mean.
A similar problem is given at https://brainly.com/question/13446621
