Question

Seventeen individuals are scheduled to take a driving test at a particular DMV office on a certain day, seven of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time.

a.) Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2).(Round your answers to four decimal places.)

P(X = 2) =

P(X ≤ 2) =

P(X ≥ 2) =

b.) Calculate the mean value and standard deviation of X. (Round your answers to three decimal places.)

mean ________individuals

standard deviation _______ individuals

Answer 1

here this is hypergeometric distribution with parameter:
sample size n=	6
population N=	17
success size k=	7

a)

probability =

P(X=2)=

(kCx)(N-kCn-x)/(NCn) =

0.3563

probability =

P(X<=2)=

∑x=0x     (kCx)(N-kCn-x)/(NCn) =

0.5158

probability =

P(X>=2)=

1-P(X<=1)=

1-∑x=0x-1     (kCx)(N-kCn-x)/(NCn) =

0.8405

b)

mean μ=nk/N =

2.471

std deviation σ=√((nk/N)*(1-k/N)*(N-n)/(N-1)) =

1.000