问题170: A bank located in a residential area is concerned about the peak hour service between noon and 2:00PM. The waiting time, in minutes, has been c

A bank located in a residential area is concerned about the peak hour service between noon and 2:00PM. The waiting time, in minutes, has been collected from a sample of 15 customers during the peak hour.

9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35
10.49 6.68 5.64 4.08 6.17 9.91 5.47

(a) Compute the mean, standard deviation and range.
(b) The bank would like to use an AI machine to shorten the waiting time to enhance the service provided. The vendor claims that their AI machine would shorten waiting times by $15 \%$ on average after on-site testing in a bank. Is it possible to have the average waiting time not to exceed 5 minutes? Please state your reason(s).
(c) Classify the sampling method in the following cases.
(i) The $8^{\text {th }}$ customer entering the bank and every $20^{\text {th }}$ customer thereafter was asked to indicate the number of credit cards in his/her wallet.
(ii) Researchers divided the customers into six groups according to gender (male or female) and monthly income group (high, medium or low). $2 \%$ of customers from each group were selected and interviewed to determine if he/she applied personal loan in the last year.
(d) Referring to part (c), state whether the data collected (which are underlined) is numerical or categorical variable and further indicate it is discrete, continuous, nominal, or ordinal.