Detecting gypsy moths 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. Each month, an SRS of 50 traps is inspected, the number of moths in each trap is recorded, and the mean number of moths is calculated.
Based on years of data, the distribution of moth counts is discrete and strongly skewed, with a mean of 0.5 and a standard deviation of 0.7.

(a) Explain why it is reasonable to use a Normal distribution to approximate the sampling distribution of x– for SRSs of size 50.

(b) Estimate the probability that the mean number of moths in a sample of size 50 is greater than or equal to 0.6.

(c) In a recent month, the mean number of moths in an SRS of size 50 was 0.6. Based on this result, should the state agricultural department be worried that the moth population is getting larger in their state? Explain.