Assume that a distributor sells laundry detergent by the case and that each case generates $6.00 in profit.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1

    Assume that a distributor sells laundry detergent by the case and that each case generates  $6.00 in profit. The sale of wine is considered random. Sales data for the last 200 days is given in the following      

   Table. 

Cases of wine sold over the last 200 days.
Case of detergent sold per day	10	11	12	13	Total days
Days this amount of detergent is sold	30	40	80	50	200

 

Required 

A)  Calculate the mean cases value (Expected value) 

B)  Calculate the cases variance 

C)  Calculate the standard deviation of cases 

   D)  Estimate the future profit per day

Question 2

Alemayehu operates a car leasing business. He is developing his budgets for the following year and is proposing to use historical data for estimating his profits for the coming year. For the previous year he has accumulated data from his car leasing business. This data shown below gives the number of cars leased, and the number of days at which this level of cars are leased during 250 days per year when the leasing company is opened.

 

 

Car leasing business
Car leased	Days at this level
20	2
21	9
22	12
23	14
24	14
25	18
26	24
27	26
28	29
29	27
30	25
31	20
32	15
33	8
34	6
35	1

 

Required 

A)  Using the data from the agency, what is a reasonable estimate of the average number of cars leased per day during the year the analysis was made?

B)  If each car leased generates $22 in profit, using the average value from the data, what is a reasonable estimate of annual profit for the coming year?

 

Question 3

 

  Blen owns a gift shop in Addis Ababa. Last year she evaluated that the probability of a customer who says they are just browsing buys something, is 30%. Suppose that on a particular day this year 15    customers browse in the store each hour.

Required 

Assuming a binomial distribution, respond to the following questions.

 

     A)  What is the probability that at least one customer, who says they are browsing, will buy something during a specified hour?

    B)  What is the probability that at least four customers, who say they are browsing, will buy something during a specified hour? 

C)  What is the probability that no customers, who say they are browsing, will buy something during a specified hour?

D)  What is the probability that no more than four customers, who say they are browsing, will buy something during a specified hour?

 

Question 4 

 

A food company processes water into 1.5 liter PET bottles. The speed of the bottling line is very high and historical data indicates that after filling, 0.15% of the bottles are ejected. This filling and ejection operation is considered to follow a Poisson distribution.

 

Required

 

     A)  What is the probability that for 2,000 bottles, none are ejected from the line? 

B)  What is the probability that for 2,000 bottles, exactly four are ejected from the line? 

C)  What is the probability that for 2,000 bottles, at least four are ejected from the line?

   D)  What is the probability that for 2,000 bottles, less than four is ejected from the line?

Question 5

A historic church site wishes to add a door to the crypt (chamber). The door opening for the crypt is small and the church officials want to enlarge the opening such that 95% of visitors can pass through without stopping (bending). Statistics indicate that the adult height is normally distributed, with a mean of 1.76 m, and a standard deviation of 12 cm.

 

Required

 

A)  Based on the design criterion, what height should the doors be made to the nearest cm? 

   B)  If after consideration, the officials decided to make the door 2 cm higher than the value obtained in Question 1, what proportion of the visitors would have to stoop when going through the door?

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