Online food delivery services. Research published in the International Journal of Consumer Studies (2020) records the distinctive characteristics of customers who did and did not order food through Online Food Delivery services (OFDs) during the COVID-19 outbreak in India. The research uses binary logistic regression to examine the respondents’ characteristics, such as age, patronage frequency before the lockdown, affective and instrumental beliefs, product involvement and perceived threat to examine the significant differences between the two categories of OFD service customers. Table 1 in the paper depicts the characteristics of the 462 respondents, listing the frequency and percentage of ordering food online by the respondents before lockdown. By grouping the responses, the data are presented as a relative frequency table as follows Times …5 6 to 10 11 to 15 16 to 20 21 to 30 Relative Frequency .745 .195 .032 .024 .004

a. Why do the relative frequencies in the table represent the approximate probabilities of the number of times a randomly selected OFD service customer ordered food online falling into a particular interval?

b. For each group, assign its value to be the maximum possible value in that group. Let x be the random variable which takes on these assigned values with the probabilities shown in the table. Find E1x2 and interpret its value in the context of the problem.

c. Find the standard deviation of x.

d. According to Chebyshev’s Rule in Chapter 2, what percentage of OFD service customers would be expected to fall within m { s? Within m { 2s?

e. What is the actual number of OFDs customers that fall within m { s? m { 2s? Compare your answers with those of part

d. Are the answers consistent?