Question

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

Answer 1

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