Respuesta :
Answer:
X has an hypergeometric distribution, with parameters:
Size of the population is N = 18.
Size of the sample is n = 6.
Number of successes n is k = 8.
Step-by-step explanation:
The people 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]
Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be taking the test for the first time.
This means that [tex]N = 18, k = 8[/tex]
We consider a success being a person taking the test for the first time, because X is the number among the six who are taking the test for the first time.
Suppose that six of these individuals are randomly assigned to a particular examiner.
This means that [tex]n = 6[/tex]
a. What kind of a distribution does X have (name and values of all parameters)
X has an hypergeometric distribution, with parameters:
Size of the population is N = 18.
Size of the sample is n = 6.
Number of successes n is k = 8.
