The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths per trap is only 1.2, but some traps have several moths. The distribution of moth counts in traps is strongly right skewed, with standard deviation 1.4. A random sample of 60 traps has x = 1 and s = 2.4.

Let X = the number of moths in a randomly selectd trap

(a) For the population distribution, what is the ...

...mean? =
...standard deviation? =

(b) For the distribution of the sample data, what is the ...

...mean? =
...standard deviation? =

(c) What shape does the distribution of the sample data probably have?

Exactly NormalApproximately Normal Right skewedLeft skewed

(d) For the sampling distribution of the sample mean with n = 60, what is the ...

...mean? =
...standard deviation? = (Use 3 decimal places)

(e) What is the shape of the sampling distribution of the sample mean?

Left skewedApproximately Normal Right skewedExactly Normal

(f) If instead of a sample size of 60, suppose the sample size were 10 instead. What is the shape of the sampling distribution of the sample mean for samples of size 10?

Approximately normalSomewhat left skewed Exactly NormalSomewhat right skewed

(g) Can we use the Z table to calculate the probability a randomly selected sample of 10 traps has a sample mean less than 1?

No, because the sampling distribution of the sample mean is somewhat right skewedYes, by the Central Limit Theorem, we know the sampling distribution of the sample mean is normal