A quality control expert at a large factory estimates that 5% of all the batteri
ID: 3134563 • Letter: A
Question
A quality control expert at a large factory estimates that 5% of all the batteries produced at the factory are defective. (The other 95% are not defective.) Six batteries are randomly selected and then each is tested to see if it's defective. Use this situation to answer the parts below.
(c) Construct the complete binomial probability distribution for this situation in a table out to the right. (d) Using your table, find the probability that exactly one of six randomly selected batteries is defective. (e) Find the probability that at least two of the six batteries selected are defective. (f) Find the probability that less than two are defective. (g) Find the mean and standard deviation of this binomial probability distribution. (h) By writing a sentence, interpret the meaning of the mean value found in (g) as tied to the context of defectiveness among six randomly chosen batteries. (i) Is it unusual to have all six of the batteries selected be defective? Briefly explain your answer giving supporting numerical evidence.Explanation / Answer
c)
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 = 6
p = the probability of a success = 0.05
x = the number of defectives
Hence, the table:
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d)
From the table,
P(1) = 0.232134281 [ANSWER]
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e)
From the table,
P(at least 2) = 1 - P(0) - P(1) = 1 - 0.735091891 - 0.232134281 = 0.032773828 [ANSWER]
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f)
From the table,
P(less than 2) = P(0) + P(1) = 0.735091891 + 0.232134281 = 0.967226172 [ANSWER]
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x P(x) 0 0.735092 1 0.232134 2 0.030544 3 0.002143 4 8.46E-05 5 1.78E-06 6 1.56E-08