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 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7.

(a) What are the mean and standard deviation of the average number of moths x⎯⎯⎯x¯ in 65 traps?
(b) Use the central limit theorem to find the probability that the average number of moths in 65 traps is greater than 0.4.

Answer 1

µ = 0.5

a) n = 65

Mean of average number of moths = µ = 0.5

Standard deviation of average number of moths = sd / sqrt(n) = 0.7 / sqrt(65) = 0.09

b)

                            

                             = P(Z > -1.15)

                             = 1 - P(Z < -1.15)

                             = 1 - 0.1251

                             = 0.8749