Reference no: EM133328120

Question 1: In a survey to find the main causes of lateness in a factory's work force, a random sample of 200 employees who were late for work were asked the reason why. The chart below shows the results.

Use the chart above to answer the following questions:

(a) What is the major cause of late coming?

(b) How many of the latecomers said delays at the security gate caused their lateness?

(c) What percentage of latecomers blamed the security gate?

(d) What percentage of latecomers blamed traffic congestion?

(e) How many of the main causes does it take to account for 80% of the problems?

(f) How many employees are affected by the problems identified in (e)?

(g) What combined percentage of late comers blamed trains and buses?

Question 2: The Football Association of Zambia (FAZ) has four football games on a particular match day. The Association wants to assign a team of officials each of the four games in a way that will minimize the total distance traveled by the officials. The distances in Kilometers for each team of officials to each game location are shown in the table below:

Table

Game Site
Officials	Ndola	Lusaka	Solwezi	Kitwe
A	210	90	180	160
B	100	70	130	200
C	175	105	140	170
D	80	65	105	120

1. How should each team of officials be assigned to a match so that the total distance travelled is minimized? Each team of officials must handle only one match.
2. Find the minimum assignment distance.
3. A major conference of accountancy is held in Johannesburg. 1200 delegates attended the conference. Out of these 60 Came from Zambia a 24 from Botswana. What is the probability that a delegate is chosen random from the audience will have come from either Zambia or Botswana?

Question 3: The occurrence of rain in Lusaka city is dependent upon whether or not it rained on the previous day.  If it rained on the previous day, the rain distribution is given below:

Event	Probability
No rain	0.50
1 cm. Rain	0.25
2	0.15
3	0.05
4	0.03
5	0.02

If it did not rain the previous day, the rain distribution is given by:

Event	Probability
No rain	0.75
1 cm. Rain	0.15
2	0.06
3	0.04

Required:

1. Simulate the city's weather for 10 days and determine by simulation the total days without rain as well as total rainfall during the period.  Use the following random numbers: 67, 63, 39, 55, 29, 78, 70, 06, 78, 76 for simulation. Assume that for the first day of simulation it had not rained the day before.

Question 4:

1. People arrive randomly at a bank teller at an average rate of 30 an hour. If the teller takes an average of 0.5 minutes to serve each customer.
   1. What is the average number of customers in the queue?
   2. How long do the customers have to wait to be served?
   3. What happens if average service time increases to 3 minutes?
2. The number of emergency admissions each day to a hospital is found to have a poison distribution with mean 2.
   1. Calculate the probability that on a single day there will be no emergency admissions.
   2. At the beginning of one day the hospital has five beds available for emergencies. Calculate the probability that this will be an insufficient number for the day.
   3. Calculate the probability that there will be exactly three admissions altogether on two consecutive days.

Question 5:

(a) A company official obtained the following information on annual salary in thousands of dollars(y) and years of experience(x) for 12 technicians at various plants of the company.

Estimate the linear regression line (model) and explain its importance

(b) The graph shows the impact of vaccinations on the occurrence of whooping cough, a childhood illness, between 1940 and 1990 in Britain. Summarize the information by selecting and reporting the main features, and make comparisons where relevant. Make necessary recommendations based on your analysis

Question 6:

1. The weight of a population of women are normally distributed with mean 60 kg and standard deviation 5 kg. What is the probability that the weight of a woman chosen at random is:
   1. Less than 61 kg                                  
   2. Greater than 70 kg                              
   3. Between 61kg and 65 kg                      
   4. Less than 55 kg                                  
2. A certain brand of light bulbs has a lifetime which is normally distributed with mean 1500 hours and a standard deviation 50 hours. What should the guaranteed life time of the bulbs be so that only 5% of the bulbs will have to be replaced under guarantee?       

Question 7:

1. A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as K 10,500 and K 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres per hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximize the total profit of the society?
2. Define a time series and discuss its four main components