Suppose we have a population that does not follow the normal distribution. What minimum sample size we should select in order to have an approximately normal distribution (symmetric) ? A. more than 10% of population size. B. it is based on population standard deviation C. 20 D. 30

Question

Mathematics

Ashtyn Andersen

25 October, 07:15

Suppose we have a population that does not follow the normal distribution. What minimum sample size we should select in order to have an approximately normal distribution (symmetric) ? A. more than 10% of population size. B. it is based on population standard deviation C. 20 D. 30

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Answers (1)

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Colby Krueger · Answer 1

D. 30

Step-by-step explanation:

Having a population that doesn't follow normal distribution (skewed) can still have sampling distribution that is completely normal. This fact is presented in the Central Limit Theorem.

Central Limit Theorem: states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, we just need to take a large sample.

So how much sample size do we need?

There is no straight forward answer to this rather we have to analyse the situation closely!

1. If the population distribution is already normal then a smaller sample size would be enough to ensure normal distribution.

2. If the population distribution is very skewed than a larger number of sample size is needed to ensure normal distribution. The rule of thumb is to take sample size equal to or more than 30 to be on safer side. This is the case in this problem hence option D fits the best.