Question

The wingspans of a common species of housefly are normally distributed with a mean of 15 mm and a standard deviation of 0.5 mm Suppose that a biologist regularly collects random samples of 20 of these houseflies and calculates the sample mean wingspan from each sample. What will be the shape of the sampling distribution of the sample mean wingspan?

Answer 1

Using the Central Limit Theorem, it is found that the shape of the sampling distribution of the sample mean wingspan is normal.

What is the Central Limit Theorem?

It states that the sampling distribution of sample means of size n, from a normally distributed population with mean $\mu$ and standard deviation $\sigma$, is normally distributed with mean $\mu$ and standard error $s = \frac{\sigma}{\sqrt{n}}$.

Hence, applying the Central Limit Theorem in this problem, the shape of the sampling distribution of the sample mean wingspan is normal.

More can be learned about the Central Limit Theorem at brainly.com/question/24663213