Respuesta :
Answer:
0.207 = 20.7% probability that exactly 10 of these are from the second section
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used.
Hypergeometric distribution:
The probability of x sucesses 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 sucesses.
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]
In this question:
20 + 30 = 50 total students, which means that [tex]N = 50[/tex]
30 students from the second section, which means that [tex]k = 30[/tex]
First 15 graded projects, so sample of 15, which means that [tex]n = 15[/tex]
a. What is the probability that exactly 10 of these are from the second section
This is P(X = 10).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 10) = h(10,50,15,30) = \frac{C_{30,10}*C_{20,5}}{C_{50,15}} = 0.207[/tex]
0.207 = 20.7% probability that exactly 10 of these are from the second section
