Answer:
Step-by-step explanation:
Hello!
X: number of gypsy moths in a randomly selected trap.
This variable is strongly right-skewed. with a standard deviation of 1.4 moths/trap.
The mean number is 1.2 moths/trap, but several have more.
a.
The population is the number of moths found in traps places by the agriculture departments.
The population mean μ= 1.2 moths per trap
The population standard deviation δ= 1.4 moths per trap
b.
There was a random sample of 60 traps,
The sample mean obtained is X[bar]= 1
And the sample standard deviation is S= 2.4
c.
As the text says, this variable is strongly right-skewed, if it is so, then you would expect that the data obtained from the population will also be right-skewed.
d. and e.
Because you have a sample size of 60, you can apply the Central Limit Theorem and approximate the distribution of the sampling mean to normal:
X[bar]≈N(μ;σ²/n)
The mean of the distribution is μ= 1.2
And the standard deviation is σ/√n= 1.4/50= 0.028
f. and g.
Normally the distribution of the sample mean has the same shape of the distribution of the original study variable. If the sample size is large enough, as a rule, a sample of size greater than or equal to 30 is considered sufficient you can apply the theorem and approximate the distribution of the sample mean to normal.
You have a sample size of n=10 so it is most likely that the sample mean will have a right-skewed distribution as the study variable. The sample size is too small to use the Central Limit Theorem, that is why you cannot use the Z table to calculate the asked probability.
I hope it helps!
