Please explain :) The gypsy moth is a serious threat to oak and aspen trees. A s
ID: 3383392 • Letter: P
Question
Please explain :)
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 0.5 , but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.5 .
What is the mean (±0.1) of the average number of moths x¯ in 60 traps? __________?
And the standard deviation? (±0.001) ___________?
Use the central limit theorem to find the probability (±0.01) that the average number of moths in 60 traps is greater than 0.8 : ___________?
Explanation / Answer
a)
What is the mean (±0.1) of the average number of moths xbar in 60 traps?
mean=0.5
b)
standard deviation = s/n
=1/sqrt(60)
=0.1290
P(X > 0.8) = (0.8-0.5)/0.129= 0.3/0.129 = 2.3256
= P ( Z >2.326) From Standard Normal Table
= 0.01