Respuesta :
Answer:
The standard deviation of the number of education majors in the sample is of 3.34.
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Standard deviation:
The standard deviation of the hypergeometric distribution is:
[tex]\sigma = \sqrt{\frac{nk}{N}(1 - \frac{k}{N})(\frac{N-n}{N-1})}[/tex]
In this question:
300 freshmen means that [tex]N = 300[/tex]
110 are education majors, which means that [tex]k = 110[/tex]
60 are chosen, which means that [tex]n = 60[/tex]
Find the standard deviation of the number of education majors in the sample.
[tex]\sigma = \sqrt{\frac{60*110}{300}(1 - \frac{110}{300})(\frac{240}{299})} = 3.34[/tex]
The standard deviation of the number of education majors in the sample is of 3.34.
