data represent the time (in minutes) recorded for a sample of 20 employees in order to get to work using public transportation.

Question One

The following data represent the time (in minutes) recorded for a sample of 20 employees in order to get to work using public transportation.

 Where the average number of days required for supplier A to deliver orders = 10.3 days and Standard Deviation = 0.67 day

1)    Which supplier provides more consistent and homogenous delivery times A or B? Justify your answer.      

2)    And do you think the delivery time for each supplier is symmetric. Support your answer with a proper test for skewness.    

Question Three

The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £².

1)    If the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

2)    In a sample of 100 customers, what are the number of customers whose expenditure is between 420 £ and 485 £?

3)    What is a probability of selecting a customer whose expenditure differs than the population expenditure by at most 50 £?

4)    In a sample of 49 customers, what are the number of customers whose mean expenditure is at least 410 £?

5)    What are the values between which the expenditure of 95% of population exist?

Table (1)

Question Five

HR manager in L&B real-state company is working with finance department in improving the salaries and the following descriptive statistics were obtained. 

Table (2)

CoefVar stands for coefficient of variation 

The company has hired you to answer the following questions:

1)    Find the missing values of (a), (b) and (c).

2)    Do you think that the salaries in the departments are skewed, justify your answer with proper measure from table (2).    3)    Based on the boxplot for the salaries by department in graph (1), comment on the graph in terms of existence of

outliers, skewness and which department has higher outliers.

4)    Based on your answer in (3), comment and compare on the suitable central and absolute dispersion measures depending on table (2).                                                                                             

5)    Based on table (1), do you think the salaries of which group is more homogenous, support your answer and comment on the results. 

Question Six

The following table gives the experience (in years) and the number of stocks sold during the previous three months by seven brokers in the Egyptian stock market.