QUESTION 1

 (i)  Describe and distinguish between discrete and continuous variable.

(ii)  A KFC shop in Port-Louis has developed an improved process for serving customers during 11.30 am to 12.30 pm peak lunch period. The waiting time in minutes (operationally defined as the time customers enters the line to when he or she is served) of all customers during this hour is recorded over a time of a week. A random sample of 15 customers is selected, and results are as follows-

8.02  4.08  5.79  8.73  5.47

5.64  8.01  10.49  8.35  5.9

9.66  9.91  3.82  6.68  6.17

a)  Compute the arithmetic mean, median, mode, first quartile and third quartile.

b)  Compute the range and interquartile range.               

c)  Compute the variance, standard deviation and a coefficient of variation.

d)  Are data distorted?               

e)  As a customer walks into restaurant throughout lunch hour, she asks the restaurant manager how long she expects to wait. The manager replies, ‘almost certainly not longer than 5 minutes’. On the basis of the results of (a) and (b), evaluate the accuracy of this statement.

QUESTION 2

 A company has made an effort to solicit new accounts from UTM students. Assume that a sample of 200 students at UTM indicate following information as to whether the student possessed a bank credit card or a travel and entertainment card-

                                       Travel and Entertainment credit card 

                                                Bank Credit Card        YES  NO      

                                                           YES              60     60    

                                                           NO               15     65    

a). Give an example of a simple event.                   

 b). Give an example of a joint event.                    

 c). what is the complement of having a bank credit card?

 d). If a student is selected at random, what is the probability that 

 i. the student has a bank credit card?                  

 ii. the student has a travel and entertainment credit card?            

 iii. the student has a bank credit card and travel and entertainment card? 

iv. the student has neither a bank credit card nor a travel and entertainment card?                            

v. the student has a bank credit card or has a travel and entertainment card?

vi. The student does not have a bank credit card or has a travel and entertainment card?                        

QUESTION 3

 The manager of a shop (store AB) wants to study characteristics of customers. In particular he decides to focus on two variables-The amount of money spent by customers on clothes and whether the customers have one child, two children or more than two children. The results from a sample of 70 customers are as follows-

 Amount of money spent: X= Rs 21.34, S= Rs 9.22

37 customers have only one child

26 customers have two children

7 customers have more than two children

a)  Set up a 95 percent confidence interval estimate of the population mean quantity spent at the shop.                 

 b)  Set up a 90 percent confidence interval estimate of the population amount of customers who have two children.          

If the manager of another shop wants to conduct an alike survey and does not have access to the information generated by manager from the store AB.

 c)  If he wants to have 95 percent confidence of estimating the true population mean amount spent in his store to within ± Rs1.50 and standard deviation is assumed to be within Rs10, what sample size is required?     

d)  If he wants to have 90 percent confidence of estimating population proportion of customers who have two kids to be within ±0.045, what sample size is essential?