9. Suppose that X is the number of defective items in a shipment of 30. a. In mo

Question

9. Suppose that X is the number of defective items in a shipment of 30. a. In most cases the appropriate statistical model for X would be the ____________________ distribution. b. Using Table A find each of the following:

i. P(X>7)=

ii P(4 (less than or equal to) X (less than or equal to) 11) =

Table A:

x F(x) 0 0.000179 1 0.001964 2 0.010596 3 0.037449 4 0.09787 5 0.202598 6 0.348054 7 0.51429 8 0.673599 9 0.803407 10 0.894272 11 0.949342 12 0.978406 13 0.991821 14 0.99725 15 0.999181 16 0.999784 17 0.99995 18 0.99999 19 0.999998 20 1 21 1 22 1 23 1 24 1 25 1 26 1 27 1 28 1 29 1

Explanation / Answer

9.

a)

Usually, we use the

binomial distribution [ANSWER]

as the probability of defect is almost constant, and the number of trials is constant (30).

b)

i.
Note that

P(x<7) = P(x<=6) = F(6)

Hence,

P(x<7) = 0.348054 [ANSWER]

***************************

ii.

Note that

P(4 <= x <= 11) = P(x<=11) - P(X<=3) = F(11) - F(3)

Thus,

P(4 <= x <= 11) = 0.949342 - 0.037449 = 0.911893 [ANSWER]

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