Question

Seventeen individuals are scheduled to take a driving test at a particular DMV office on a...

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

Homework Answers

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
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