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Answer: Probability that the entire batch will be rejected is 0.611.
Step-by-step explanation:
Since we have given that
Number of clock radios in a batch = 8000
Probability of defective clock radio = 7%
According to question, we have mentioned that A sample of 13 clock radios is randomly selected without replacement from the 8,000 and tested.
We will use "Binomial distribution":
here, n = 13 and
p (probability of success) = 7% = 0.07
so, we need to find that
P(the entire batch will be rejected) = P(at least one of those test is defected)
So, it becomes,
P(at least one of those tested is defective) = 1 - P(none are defective)
So, P(none are defective ) is given by
So, P(at least one of those tested is defective) = 1 - P(none are defective)
= 1 - 0.389
= 0.611
Hence, Probability that the entire batch will be rejected is 0.611.