2.10 The Hypergeometric Random Variable; Acceptance Sampling
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Exercises 2.10
1. A lot of 50 fuses is known to contain 7 defectives. A random sample of size 10 is
drawn without replacement. What is the probability the sample contains at least 1 defective fuse?
2. A collection of 30 gems, all of which are identical in appearance and are supposed to
be genuine diamonds, actually contains 8 worthless stones. The genuine diamonds are valued at 1200 each. Two gems are selected.
a. Let X denote the total actual value of the gems selected. Find the probability
distribution function for X.
b. Find E. X. 3. a. A box contains 3 red and 5 blue marbles. The marbles are drawn out one
at a time and without replacement, until all of the red marbles have been selected. Let X denote the number of drawings necessary. Find the probability
distribution function for X.
b. Find the mean and variance for X. 4. a. A box contains 3 red and 5 blue marbles. The marbles are drawn out one at
a time and without replacement, until all the marbles left in the box are of the same color. Let X denote the number of drawings necessary. Find the
probability distribution function for X.
b. Find the mean and variance for X. 5. A lot of 400 automobile tires contains 10 with blemishes which cannot be sold at
full price. A sampling inspection plan chooses 5 tires at random and accepts the lot only if the sample contains no tires with blemishes.
a. Find the probability that the lot is accepted. b. Suppose any tires with blemishes in the sample are replaced by good tires if
the lot is rejected. Find the average outgoing quality of the lot.
6. A sample of size 4 is chosen from a lot of 25 items of which D are defective. Draw
the curve showing the probability that the lot is accepted as a function of D if the lot is accepted only when the sample contains no defective items.
7. A lot of 250 items that contains 15 defective items is subject to an acceptance
sampling plan that calls for a sample of size 6 to be drawn. The lot is accepted if the sample contains, at most, one defective item.
a. Find the probability that the lot is accepted. b. Suppose any defective items in the sample are replaced by good items. Find
the average outgoing quality.
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Chapter 2 Discrete Random Variables and Probability Distributions