Respuesta :
Answer:
Mean is 19.43
Standard deviation is 2.5322
Step-by-step explanation:
For each student who graduated from high school in 2012, there are only two possible outcomes. Either they have enrolled in college, or they have not. The probability of a student having enrolled in college is independent of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
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]
67% of students who graduated from high school in 2012 enrolled in college.
This means that [tex]p = 0.67[/tex]
Sample of 29 high school graduates
This means that [tex]n = 29[/tex]
Mean
[tex]E(X) = np = 29*0.67 = 19.43[/tex]
Standard deviation
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{29*0.67*0.33} = 2.5322[/tex]
