1112 Detecting gypsy moths The gypsy moth is a serious threa

11.12 Detecting gypsy moths. The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department place 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 count is discrete and strongly skewed, with standard deviation 0.7

(a). What are the mean and standard deviation of the average number of moths in 50 random traps?

(b). Use the Central Limit Theorem to find the probability that the average number of moths in 50 traps is more than 0.6.

Solution

(a). What are the mean and standard deviation of the average number of moths in 50 random traps?

mean =0.5 (stay the same)

standard deviaton =s/vn

=0.7/sqrt(50)

=0.09899495

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(b). Use the Central Limit Theorem to find the probability that the average number of moths in 50 traps is more than 0.6.

P(xbar>0.6) = P((xbar-mean)/(s/vn) >(0.6-0.5)/0.09899495)

=P(Z>1.01) = 0.1562 (from standard normal table)