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GE2262 Business Statistics, 2020/21 Semester B Individual Assignment 1

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- 1 - Name: KAWLE shreyash sanjay Student No.: 56318142 EID: sskawle2 Tutorial Session Code: T03 GE2262 Business Statistics, 2020/21 Semester B Individual Assignment 1 Instructions: 1. Fill in your particulars at the top of this page. 2. Answer all questions in the space provided below. 3. Show all calculations clearly. 4. Display all non-integer numeric values to 4 decimal places. 5. Late submission penalty: deduct 10% of the base score per day. Question 1 (15 marks) The following table shows the percentage decreases in share values for the thirty largest common stock mutual funds in Hong Kong on 12 September 2001 after the aircraft attacked on the World Trade Centre in New York. 4.1 6.0 5.8 3.9 3.8 3.9 3.0 4.9 5.2 4.2 3.3 5.6 3.3 3.6 10.5 4.4 5.4 4.3 4.4 3.5 3.3 3.8 6.4 8.6 4.7 10.4 4.0 4.7 7.2 3.7 (a) Compute the median and mode of the data. (2 marks) (b) Find the mean, standard deviation and variance of the data. (3 marks) - 2 - (c) Determine the range, interquartile range of the data. (2 marks) (d) List the five-number summary of the data. Form the box-and-whisker plot. Are the data skewed? If so, how? (5 marks) - 3 - (e) What percentage of the data within ±1, ±2 and ±3 standard deviation of the mean? (3 marks) Question 2 (5 marks) A team of consultants studied the service operation at City Bank. They measured the time between customer arrivals to the bank over the course of a day. After several months, the probability distribution of the number of customer arrivals (per 15 minutes) was developed: Number of customers 16 17 18 19 20 21 Probability 0.1 0.2 0.3 a 0.1 0.1 (a) Find the value of a. (1 mark) (b) Calculate the expected number of customer arrivals. (2 marks) - 4 - (c) Find the probability that the number of customer arrivals is more than 18. (2 marks) Question 3 (10 marks) The director of a large employment agency wishes to study various characteristics of its job applicants. A sample of 200 applicants has been selected for analysis. Seventy applicants have had current jobs for at least five years; 80 of the applicants are college graduates; 25 of the college graduates have had their current jobs at least five years. What is the probability that an applicant chosen at random: (a) is a college graduate? (2 marks) (b) is a college graduate and has held the current job less than five years? (2 marks) (c) is a college graduate or has held the current job at least five years? (3 marks) - 5 - (d) has held the current job at least five years given that he/she is not a college graduate? (3 marks) Question 4 (20 marks) The test marks of a population of students are normally distributed with mean 65 and standard deviation ?. The passing mark is 60. Five percent of the students got 90 or above. (a) Find the value of ?. (4 marks) (b) A student is selected at random. Find the chance that he/she passes the test. (3 marks) - 6 - (c) What is the minimum mark needed in order to be in the top 15% of all students taking the test? (3 marks) (d) What is the probability of a randomly selected student with test mark 75? (2 marks) - 7 - (e) For a randomly chosen student, state, without doing the calculations, in which of the following ranges his or her mark is most likely to be: A. 60-70, B. 70-80, C. 80-90, D. 90-100. (2 marks) For a randomly selected student his or her marks is most likely to be (A) 60 - 70, because mean value is 65 and around this value the probability would be highest. (f) Suppose 10 students are randomly selected. What is the chance that at least 2 of them pass the test. (6 marks)

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