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)
\(P(X\in {25,26,27,28,29,30})
=\sum_{i=25}^{30}\left(\begin{matrix}50 \\ i\end{matrix}\right)0.7^i 0.3^{50-i}\)
=0.001436+0.003223+0.006684+0.012811+0.022677
=0.037039