In Exercise 2.33 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 accompanying file. For this exercise, consider these interarrival times to represent the population of interest.
a. In Exercise 2.33 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 , the sample mean. Theoretically, what are µ and σ?
d. Find P( < 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 . (Every student in the class should do this.)
f. Refer to part e. Obtain the values of x computed by the I students and combine them into a single data set. Form a histogram for these values of . Is the shape approximately normal?
g. Refer to part f. Find the mean and standard deviation of the x-values. Do these values approximate µ and σ respectively?