It is claimed that 10% of the computer chips coming from an assembly line are de
ID: 3124916 • Letter: I
Question
It is claimed that 10% of the computer chips coming from an assembly line are defective. Assume the conditions of successive parts from this line are independent. X is the number of the next 10 from this line that are defective. (a) Show that X meets the condition to be binomial and identify n and p. (b) How many of the 10 does one expect to be defective, i.e., compute E(X)? (c) One repeats this process 100 times, i.e., 100 times the next 10 chips are examined, and the numbers of defectives for the 100 repetitions are averaged. Approximately, what would this average be? (d) Using the formula on page 67, compute P[X = 4].
If 4 of the next 10 chips are defective, based on the probability in part (a), would you (i) believe the claim that 10% are defective (ii) be neutral concerning this claim or (iii) suspect the claim is false
Explanation / Answer
a)
There are constant number of trials, n = 10.
The trials are independent.
There are only 2 categories, defective and nondefective.
The probability of dfective parts is the same for all parts.
Hence, it satisfies the conditions.
Here,
n = 10, p = 0.10.
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b)
E(x) = n p = 10*0.10 = 1 [ANSWER]
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c)
It would be approximately 1, as that is the xpected value. [ANSWER, 1]
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d)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 10
p = the probability of a success = 0.1
x = the number of successes = 4
Thus, the probability is
P ( 4 ) = 0.011160261 [ANSWER]
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e)
If it's solely based on part d, we ii) be netral concerning this claim.
Why? Because our basis should be P(x>=4), not P(x = 4).
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