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 0.9.

What is the mean (±0.1) of the average number of moths x⎯⎯⎯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 0.4:     

Answer 1

µ = 0.4

sd = 0.9

a) n = 60

mean of the average number of months = µ = 0.4

Standard deviation of number of months = sd / sqrt(n) = 0.9 / sqrt(60) = 0.116

b)

                              

                               = P(Z > 0)

                               = 0.5