GM03

BUSINESS STATISTICS

Assignment – I

Assignment Code: 2014GM03A1        Last Date of Submission: 15th April 2014

                                                      Maximum Marks: 100

Attempt all the questions. All the questions are compulsory and carry equal marks.

Section‐A

1.        a) Collect 40 days of data for the amount of time you talk on your mobile phone each day in minutes and develop a frequency distribution for the same. Based on the same calculate the mean, median, mode (if any), standard deviation.

b)   Draw a suitable pictorial way of representing the data collected by you above.

2.        a)   The probability of catching cold during the winter’s is known to be 0.40. If 10 people are        randomly selected, what is the probability that this sample will contain at least two people with cold.

b)   If the number of people sampled had been 40 and the probability of catching cold had been only 2% what is the probability that the number of people with cold would be less than 7.

3.        a)   Identify the appropriate scale in which the following data will be collected.

   (i)        color code of dresses of volunteer in relief operation.

   (ii)        performance of relief agencies on a scale of 1 to 10.

  (iii)        ranking of various relief items in terms of criticality

  (iv)        rainfall in a city for the last five years.

b)         25% of the applicants for a job are known to overrate themselves in their CV. While going for an interview, 50% of those who overrate themselves somehow manage to get selected and only 20% of those who do not overate themselves manage to get themselves selected for the job . Given that the person got selected for the job what is the probability that he had overrated his CV.

4.        a)        The amount of calories burnt during a normal workout is believed to be normally distributed with a mean of 600 calories with a standard deviation of 180 calories.

Evaluate the following:

(i)        the proportion of persons who will burn less than 400 calories.

(ii)        the proportion of persons who will burn between 450 to 700 calories.

(iii)        the proportion of persons who will burn more than 800 calories.

b)         The proportion of invitees who attend any conference organized by the scientific community is believed to be 60%. If 600 invitees are sent letters for attending a conference, what is the probability that more than 400 invitees will attend the conference.

Section‐B 

Case Study

A company in the business of selling smart phones estimates that its customers are satisfied with its services. In a scale of 1 to 100 the company believes that it should get a rating of at least 82 points. For this purpose the company selects randomly 3000 of its customers and conducts a sample survey to determine the level of satisfaction. The average satisfaction level obtained during the survey was 76 points with a standard deviation of 18 points. Based on the above the research team decided to evaluate a confidence interval with 95% confidence.

5.        Case Questions:

a)        What will be the confidence interval for a 95% confidence level which will be evaluated by the research team.

b)        If the research team wanted the confidence level to be 99% with the same level of accuracy then what should be the sample size.

c)         based on the answer for part (a) do you think that the company expectation of getting a rating of 82% can be considered to be correct. Justify your answer.