Can anyone else answer this?
2 answers:
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Answer:
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
The batteries produced in a manufacturing plant have a mean time to failure of 30 months with a standard deviation of 2 months.
This means that
Sample of 400 batteries. The sampling distribution of is approximately:
So
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.