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 1.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 1.7.

A.)  What are the mean and standard deviation of the average number of moths x in 50 traps? (Round your mean to two decimal places and your standard deviation to three decimal places.)

B.) Use the central limit theorem to find the probability that the average number of moths in 50 traps is greater than 1.1. (Round your answer to four decimal places.)

Answer 1

From the given information,

The required correct answers are,

A. Mean=1.50

Standard deviation=1.7/squareroot(50)=0.240

B. By using calculator,

The required probability is,

P(Xbar>1.1)=0.9519

Thank you.