The distribution of the number of eggs laid by a certain species of hen during t

Question

The distribution of the number of eggs laid by a certain species of hen during their breeding period is 32 eggs with a standard deviation of 16.2. Suppose a group of researchers randomly samples 36 hens of this species, counts the number of eggs laid during their breeding period, and records the sample mean. They repeat this 10,000 times, and build a distribution of sample means. Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explain your reasoning.

Explanation / Answer

as per central limit theorum shape of distribution od sample means is symmetric if sample size>=30.

as the sample size increases, the mean do have proclivity to reach closer and closer to its true value as per law of large numbers.

hence it should be symmetric

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