A consumer agency randomly selected 1700 flights
SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT BBA240 - QUANTITATIVE METHODS ASSIGNMENT DUE: FRIDAY, 10th September, 2021 INSTRUCTIONS TO CANDIDATES: 1. Assignment can be submitted by or before the due date. 2. Submission shall strictly be through the online learning platform and NOT by email. Kindly familiarise yourself with the process. Question One (1) The following question refers to the data in the excel sheet showing 2015 GDP per capita and fertilty rates for different countries in the world. a) (i) Make a cumulative percentage graph of GDP per capita using classes of ten thousand points, starting with 1-10000. [5 marks] (ii) State the range of the GDP per capita values of countries that are below the 25th percentile? [2 marks] (iii) State the range of the GDP per capita values of countries that above the 75th percentile? [2 marks] (iv) What is the mean GDP per capita value? [1 mark] 1 b) Fertility rates for the SADC countries represent a sample of world fertility rates (population). (i) Find the sample mean and standard deviation of the fertility rates. [4 marks] (ii) Find the population mean and standard deviation of the fertility rates. [4 marks] (iii) Comment on the SADC vs World GDP per capita and fertilty rates. [2 marks] c) (i) Find the range for the world GDP per capita and fertilty rates. [4 marks] (ii) Find the median values for the world GDP per capita and fertilty rates. [2 marks] (iii) Find the interquartile range for the world GDP per capita and fertilty rates. [4 marks] [Total: 30 marks] Question Two (2) a) A consumer agency randomly selected 1700 flights for two major airlines, A and B. The following table gives the two-way classification of these flights based on airline and arrival time. Note that ”less than 30 minutes late” in- cludes flights that arrived early or on time. Less Than 30 30 Minutes to More Than Minutes Late 1 Hour Late 1 Hour Late Airline A 429 390 92 Airline B 393 316 80 If one flight is selected at random from these 1700 flights, find the probability that this flight is (i) not more than 1 hour late [1 mark] (ii) is not less than 30 minutes late [1 mark] (iii) a flight on airline B given that it is 30 minutes to 1 hour late [2 marks] (iv) more than 1 hour late given that it is a flight on airline A [2 marks] Page 2 of 5 b) Two new computer codes are being developed to prevent unauthorized access to classified information. The first consists of six digits (each chosen from 0 to 9); the second consists of three digits (from 0 to 9) followed by two letters (A to Z, excluding I and O). (i) Which code is better at preventing unauthorized access (defined as break ing the code in one attempt)? [3 marks] (ii) If both codes are implemented, the first followed by the second, what is probability of gaining access in a single attempt? [2 marks] c) A certain Mobile Money Agency is an agent for Zanaco Express, Airtel, MTN and Zamtel Mobile Money. Experience has shown that the probabilities of finding a float for withdrawals of amounts K5000 and above are given as 0.4, 0.5, 0.3 and 0.2, respectively. Experience has also shown that among his clients, the probabilities that a client requires a service from Zanaco Express, Airtel, MTN, Zamtel Mobile Money are given as 0.3, 0.4, 0.2 and 0.1, respec- tively. Assume that each client visits the agency for withdrawals from only one at a time. (i) What is the probability that a client who wishes to withdraw K5000 will not be successful? [3 marks] (ii) What is the probability that an MTN client who wishes to withdraw K5000 will not be successful? [2 marks] (iii) What is the probability that an Airtel client who wishes to withdraw K5000 will not be successful? [2 marks] (iv) A certain client has just failed to make a withdrawal of K7000, what is the probability that he/she is a Zamtel Mobile money client? [2 marks] [Total: 20 marks] Question Three (3) a) Hospital records show that of patients suffering from a certain disease, 25% die of it. (i) What is the probability that of 6 randomly selected patients, 4 will recover? [3 marks] (ii) What is the most probable number of recoveries out of 6 randomly selected patients? [2 marks] Page 3 of 5 (iii) Compute and plot a bar graph of the probability distribution of recoveries out of 6 randomly selected patients. [5 marks] (iv) Plot the distribution function of the number of recoveries out of 6 randomly selected patients. [2 marks] b) Phone calls enter the ”support desk” of an electricity supplying company on the average two every 3 minutes. If one assumes an approximate Poisson process: (i) What is the probability of no calls in 3 minutes? [2 marks] (ii) What is the probability of utmost 6 calls in a 9 minute period? [2 marks] c) Suppose the earnings of a laborer, denoted by X, are given by the following probability distribution. xi P (xi) 0 8/27 1 12/27 2 6/27 3 1/27 Find the laborer’s expected earnings and the variance of his earnings. [4 marks] [Total: 20 marks] Question Four (4) a) Sports shirts are frequently classified as S, M, L, XL for small, medium, large and extra-large neck sizes. S fits a neck circumference of less than 37cm, M fits between 37 and 40.5cm and L fits between 40.5cm and 44cm while XL fits necks over 44cm in circumference. The neck circumference of adult males has a normal distribution with µ= 40cm and σ = 2cm. (i) What proportion of shirts should be manufactured in each category? [6 marks] (ii) If you wanted to define categories S, M, L, XL so that the categories con- tained 20%, 30%, 30% and 20% respectively, of the total population of adult males, what neck sizes must you assign to each of the categories? [6 marks] Page 4 of 5 b) The life of an electronic device is known to have the exponential distribution with parameter λ = 1 1000 . (i) What is the probability that the device lasts more than 1000 hours? [2 marks] (ii) What is the probability it will last less than 1200 hours? [2 marks] (iii) Find the mean and variance of the life of the electronic device. [4 marks] [Total: 20 marks] Question Five (5) a) The average demand on a factory store for a certain electric motor is 8 per week. When the storeman places an order for these motors, delivery takes one week. If the demand for motors has a Poisson distribution, how low can the storeman allow his stock to fall before ordering a new supply if he wants to be at least 95% sure of meeting all requirements while waiting for his new supply to arrive? [6 marks] b) A bank has 175 000 credit card holders. During one month the average amount spent by each card holder totalled $192,50 with a standard deviation of $60,20. Assuming a normal distribution, determine the number of card hold- ers who spent more than $250. [4 marks] [Total: 10 marks] END! Page 5 of 5