In a batch of 27 pedometers, 3 are believed to be defective. A quality-control e

Question

In a batch of 27 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 5 units to test. Let random variable X the number of defective units that are among the 5 units tested a. Find the probability mass function f(x) P(X-x), and sketch its histogram b. Find P(X= 1). What does this number represent? c. Find P(X 2 1). What does this number represent? Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x) = P(X = x) f(x) = P(X=x)= (Simplify your answers.) a. Find the probability mass function f(x) P(X x) f(x) = (Type an ordered pair. Use a comma to separate answers as needed. Round to five decimal places as needed.) Let x-the number of defective pedometers among the 5 units tested, and let y=f(x). Choose the correct histogram below.

Explanation / Answer

total - 27

24 -undefected

3 -defected

we select 5

P(X= x) = 3Cx * 24C(5-x) /(27C5)

correct graph is C)

option C) is correct

b) option D) is correct

= (3C1 *24C4 /(27C5) = 0.39487179487

c) option D) is correct

P(X>=1) = 1 - P(X=0) = 1- (3C0 *24C5 /(27C5) = 1 -0.52649572649= 0.4735042735

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