You manage a luxury department store in a busy shopping centre. You have extremely high foot trafc (people coming through your doors), but you are worried about the low rate of conversion into sales. That is, most people only seem to look, and few actually buy anything. You determine that only 1 in 10 customers make a purchase. (Hint: The probability that the customer will buy is 1/10.) Tasks {show your workings): A. During a 1 minute period you counted 8 people entering the store. What is the probability that only 2 or less of those 8 people will buy anything? (Hint: You have to do this by hand, showing your workings. Use the formula on slide 11 of lecture 6. But you can always check your calculations with Excel to make sure they are correct.) 5. fToskA is worth the full 2 marks. But you can earn a bonus point for doing Task B.) On average you have 4 people entering your store every minute during the quiet 10-1lam slot. You need at least 6 staff members to help that many customers but usually have 7 staff on roster during that me slot. The 7\"\" staff member rang to let you know he will be 2 minutes late. What is the probability 9 people will enter the store in the next 2 minutes? (Hint 1: It is a Poisson distribution. Hint 2: What is the average number of customers entering every 2 minutes? Remember to show all your workings.) Question 1 of B You are an investment manager for a hedge fund. There are currently a lot of rumours going around about the "hot\" property market on the Gold Coast, and some of your investors want you to set up a fund specialising in Surfers Paradise apartments. You do some research and discover that the average Surfers Paradise apartment currently sells for $1.1 million. But there are huge price differences between newer apartments and the older ones left over from the 1980's boom. This means prices can vary a lot from apartment to apartment. Based on sales over the last 12 months, you calculate the standard deviation to be $385 000. There is an apartment up for auction this Satu rday, and you decide to attend the auction. Tasks l[show your workings): A. Assuming a normal distribution, what is the probability that apartment will sell for over $2 million? B. What is the probability that the apartment will sell for over $1 million but less than $1.1 million