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 greater than 30 batteries will last at least 8 hours

Answer 1

0.9152

Explanation:

Given that 50 identical batteries are being tested after 8 hours of continuous use.

Assumption is p = Probability for any bulb operating after 8 hours -=070

q= 0.30

n = number of trials = 50

X -- the no of bulbs which last more than 8 hours is binomial because

i) Each bulb is independent of the other

ii) There are only two outcomes, yes or no

Required probability = P(X>30)

=P(X=31)+P(X=31)+....+P(X=50)

=0.9159

=0.9152

Hence anwer is 0.9152

Answer 2

The probability of success is constant = p = 0.7
There are a fixed number of trials = n = 50
The trials are independent.
The sample is a simple random sample.

Thus, the given scenario satisfies all the conditions of a Binomial experiment so we will use Binomial probability to solve this problem.

We are to find the probability that greater than 30 bulbs will last atleast 8 hours.

So, we are to find P(X > 30)

We can use any Binomial calculator to find this value.

P(X> 30) comes out to be 0.9152

Therefore, the probability that greater than 30 batteries will last at least 8 hours is 0.9152.