In Exercise, you learned that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. Data from an actual phishing attack against an organization were presented in Chance (Summer 2007). The interarrival times, i.e., the time differences (in seconds), for 267 fraud box e-mail notifications were recorded and are saved in the PHISHING file. For this exercise, consider these interarrival times to represent the population of interest.

a. In Exercise 2.43 you constructed a histogram for the interarrival times. Describe the shape of the population of interarrival times.

b. Find the mean and standard deviation of the population of interarrival times.

c. Now consider a random sample of n = 40 interarrival times selected from the population. Describe the shape of the sampling distribution of x-bar, the sample mean. Theoretically, what are μx-bar and σx-bar?

d. Find P(x-bar < 90).

e. Use a random number generator to select a random sample of n = 40 interarrival times from the population, and calculate the value of x-bar. (Every student in the class should do this.)

f. Refer to part e. Obtain the values of x-bar computed by the students and combine them into a single data set. Form a histogram for these values of x-bar. Is the shape approximately normal?

g. Refer to part f. Find the mean and standard deviation of the x values. Do these values approximate μx-bar and σx-bar, respectively?