Find the indicated probabilities using the geometric distribution or Poisson dis

Question

Find the indicated probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities.
A glass manufacturer finds that 1 in every 1000
glass items produced is warped.

Find the probability that:
(A) the first warped glass item is the 11th item produced =

(B) the first warped item is the first, second, or third item produced, and

(C) none of the first 10 glass items produced are defective.

(a) P (the first warped glass item is the 11th
item produced) =
(Round to three decimal places as needed.)

(b) P(the first warped item is the first, second, or third item produced) =
Round to three decimal places as needed.)

(c) P(none of the first 10 glass items produced are defective) =
(Round to three decimal places as needed.)

Which of the events are unusual? Select all that apply.
A. The event in part (a) is unusual.
B. The event in part (b) is unusual.
C. The event in part (c) is unusual.
D. None of the events are unusual.

Explanation / Answer

Solution:

a) P (the first warped glass item is the 11th
item produced) = (999/1000)^10 *(1/1000) = 0.00099004488 = 0.001

b) P(the first warped item is the first, second, or third item produced) = 1/1000 +(999/1000) (1/1000) + (999/1000) (999/1000) (1/1000) = 0.002997001 = 0.002

c) P(none of the first 10 glass items produced are defective) = (999/1000)^10 = 0.99004488 = 0.990

Which of the events are unusual
C. The event in part (c) is unusual.

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