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Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30. What is the probability that between 25 and 30 batteries (inclusive) will last at least 8 hours

Verified Answer :

meerkat18

Given:
Bernoulli trials,
(population) success rate = p = 0.7 (constant throughout trials)
Assume independence of the 50 batteries
use binomial distribution with parameters (n,p)=(50,0.7)
P(X\in {25,26,27,28,29,30})
=0.001436+0.003223+0.006684+0.012811+0.022677
=0.037039

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