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#### Houseflies have pretty short lifespans. Males of a certain species have lifespans that are strongly skewed to the right with a mean of 26 days and a standard deviation of 12 days

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Anonymous
0

A biologist collects a random sample of 22 of these male houseflies and observes them to calculate the sample mean lifespan. We can assume that the houseflies in each sample are independent.

What will be the shape of the sampling distribution of the sample mean lifespan?

Sangeetha Pulapaka
0

The shape of the sampling distribution is unknown as it is not given. When a population is normally distributed, the sampling distribution of the sample mean \overline{x} will also be normal regardless of sample size.

n≥30 will be normally distributed, but sample means coming from small samples n<30 may not necessarily be normal.

Since the population of lifespans is skewed to the right, and our sample size of 22 houseflies is small (n<30), the sampling distribution of the sample mean will still be skewed right but will be approaching a normal distribution.

The sampling distribution of the sample mean lifespan will be skewed to the right, but less skewed than the population.

The answer is - the shape of the sampling distribution will be skewed to the right.