Question

Houseflies have pretty short lifespans. Males of certain species have lifespans that are strongly skewed to the right with a mean of 26 days and a standard deviation of 12 days. A biologist collects a random sample of 10 of those male houseflies and repeats the sampling for 50 times 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?

a) Normal

b) Skewed Left

c) Unknown

d) Skewed Right

Answer 1

The shape of the sampling distribution of the sample mean lifespan of houseflies will be normal due to the Central Limit Theorem, which applies despite the original lifespan being skewed because the biologist repeated the sampling for a number of times.

Step-by-step explanation:

The shape of the sampling distribution of the sample mean lifespan of houseflies, in this case, will tend toward a normal distribution. This outcome is a result of the Central Limit Theorem which states that the distribution of sample means will be approximately normal if the sample size is large enough, usually n > 30. However, even for sample sizes smaller than 30, if the population distribution is not strongly skewed or does not have heavy tails, the sample mean distribution will still be approximately normal.

In this case, the biologist collects random samples of 10 male houseflies and repeats the sampling 50 times.

Although the original lifespan data of the houseflies is strongly skewed to the right, the sample mean for a sufficiently large number of repeated samples (in this case, 50) will approximate a normal distribution due to the Central Limit Theorem. Therefore, the correct answer is (a) Normal.