Respuesta :
Answer:
Mean is 3.05
Standard deviation is 1.69.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they are foreign, or they are not. This means that we can solve this problem using concepts of the binomial probability distribution.
Binomial probability distribution
The probability of x sucesses on n repeated trials, with p probability.
In this problem, we have a sample of 50 students, so [tex]n = 50[/tex]. The proportion of all UNC students that are foreign students is 0.061, so [tex]p = 0.061[/tex].
The mean is given by the following formula:
[tex]E(X) = np = 50*0.061 = 3.05[/tex]
The standard deviation is given by the following formula:
[tex]\sigma = \sqrt{n*p*(1-p)} = \sqrt{50*0.061*(1-0.061))} = 1.69[/tex]
(a) The Mean of the students will be 3.05
(b) The standard deviation will be 1.69.
What will be the Mean and the standard deviation?
For every student, the possible outcomes are only two. Either they are foreign students or they are not.
Since this concept is based on Binomial probability distribution
So from Binomial probability distribution
The probability of x successes on n repeated trials, with p probability.
In this problem, we have a sample of 50 students, so [tex]n=50[/tex] The proportion of all UNC students that are foreign students is 0.061,[tex]p=0.061[/tex]
The mean is given by the following formula:
[tex]E(x)=n\times p=50\times 0.061=3.05[/tex]
The standard deviation is given by the following formula
[tex]\sigma =\sqrt{n\times p\times (1-p)[/tex]
[tex]\sigma = \sqrt{50\times 0.061\times(1-0.061)}[/tex]
[tex]\sigma =1.69[/tex]
Thus
(a) The Mean of the students will be 3.05
(b) The standard deviation will be 1.69.
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