Examine Figure 6-38, “Time Shopping.”
(a) Notice that 52% of the people who go to a shopping center spend less than 1 hour. However, the figure also states that people spend an average of 69 minutes on each visit to a shopping center. How could both these claims be correct? Write a brief, complete essay in which you discuss mean, median, and mode in the context of a symmetrical distribution. Also discuss mean, median, and mode for distributions that are skewed left, for those skewed right, and for general distributions. Then answer the following question: How could 52% of the people spend less than 1 hour in the shopping center if the average (we don’t know which average was used) time spent was 69 minutes?

(b) Ala Moana Shopping Center in Honolulu is sometimes advertised as the largest shopping center for 2500 miles and the best shopping center in the middle of the Pacific Ocean. There are many interesting Hawaiian, Asian, and other ethnic shops in Ala Moana, so this center is a favorite of tourists. Suppose a tour group of 75 people has just arrived at the shopping center. The International Council of Shopping Centers indicates that 86% (52% plus 34%) of the people will spend less than 2 hours in a shopping center. Let us assume this statement applies to our tour group.
(i) For the tour group of 75 people, what is the expected number who finish shopping on or before 2 hours? What is the standard deviation?
(ii) For the tour group of 75 people, what is the probability that 55 or more will finish shopping in 2 hours or less?
(iii) For the tour group, what is the probability that 70 or more will finish shopping in 2 hours or less?
(iv) What is the probability that between 50 and 70 (including 50 and 70) people in the tour group will finish shopping in 2 hours or less?
(v) If you were a tour director, how could you use this information to plan an appropriate length of time for the stop at Ala Moana shopping center? You do not want to frustrate your group by allowing too little time for shopping, but you also do not want to spend too much time at the center.

Transcribed Image Text:

Time Shopping People spend an average of 69 minutes each visit to a shopping center or mall. Less than 1 hour 52% 1-2 hours 34% 10% thurg 3 -2-3 hours -4% More than 3 hours