SOA Exam P Sample Question 321
Study guide: Exam P-1
A business manufactures light bulbs and sells them in boxes of 50. Let p denote the probability that a light bulb is defective. The events that different light bulbs are defective are mutually independent.
Let X denote the number of non-defective light bulbs in a box of 50. In addition, let n be an integer such that P[X \geq n] \geq 0.95.
Determine which one of the following statements must be true.
- A)
\displaystyle\sum_{k=n}^{50}\left[\frac{50!}{k!(50-k)!}\right](1-p)^k p^{50-k} \geq 0.95 - B)
\displaystyle\sum_{k=0}^{n}\left[\frac{50!}{k!(50-k)!}\right](1-p)^k p^{50-k} \geq 0.95 - C)
\displaystyle\sum_{k=n+1}^{50}\left[\frac{50!}{k!(50-k)!}\right]p^k (1-p)^{50-k} \geq 0.95 - D)
\displaystyle\sum_{k=0}^{n}\left[\frac{50!}{k!(50-k)!}\right]p^k (1-p)^{50-k} \geq 0.95 - E)
\displaystyle\sum_{k=n}^{50}\left[\frac{50!}{k!(50-k)!}\right]p^k (1-p)^{50-k} \geq 0.95
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