Question

that what also confuses me because there is no sample size given

Based on the central limit theorem: if the population mean = 2.0 kg and population standard deviation = 4 kg then we can say that the sample standard deviation equals

Answer 1

Solution :

Central limit theorem does not tells us about the sample standard deviation. It tells us about the sampling distribution of sample means and consequently it tells what will be the mean and standard deviation of the sampling distribution of sample mean.

According to central limit theorem, if we have a population with mean μ and standard deviation σ and if we take a random sample of sufficiently large size (say n > 30) from this population, then sampling distribution of sample means of all such samples of this size will be approximately normal with mean  μ and standard deviation σ/√n.

Only population mean and population standard deviation is given. We need sample size also, then only we can calculate the standard deviation of the sampling distribution of sample mean.