Question

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 trapped is only 0.4, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.6. (a) What are the mean and standard deviation of the average number of moths x in 45 traps

Answer 1

Mean = 0.4

Stand deviation = 0.08944

Explanation:

1.

This question tells us that the mean of trapped moths is only 0.4

Therefore the mean = E(X) = 0.4

2.

The standard deviation of the sample mean is

= σ/√n

σ = 0.6

n = 45

When we put these values into the formula we will have:

0.6/√45

= 0.6/6.708

= 0.08944

So in conclusion, the mean is 0.4 and the standard deviation is 0.08944.

Thank you!