Question

The lifetime of a certain type of battery has a mean value 20 hours and standard deviation 3 hours. A bulk package of these batteries contains 40 randomly selected batteries. The distribution of average life time i g

Answer 1

The distribution of average life time is approximately normallyl distributed with mean 20 hours and standard deviation of 0.4743 hours

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem

`\mu = 20, \sigma = 3, n = 40, s = (3)/(√(40)) = 0.4743`

The distribution of average life time is approximately normallyl distributed with mean 20 hours and standard deviation of 0.4743 hours