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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MBA SEMESTER- II • EXAMINATION WINTER 2018
Subject Code: 4120503 Date: 27/12/2018
Subject Name: Business Statistics
Time: 02:30 PM To 05:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Give definition of following terms:
Histograms
Frequency Polygon
Ogives
Stem Leaf Plots
Pie Charts
Pareto Charts
Scatter Plot
07

A random sample of voters in one of village in Gujarat is classified by age groups, as shown by the following data.
Age group
Frequency
18 under 24
17
24 under 30
22
30 under 36
26
36 under 42
35
42 under 48
33
48 under 54
30
54 under 60
32
60 under 66
21
66 under 72
15
a. Calculate the mean of the data
b. Calculate the mode
c. Calculate the variance
d. Calculate the standard deviation
07
Q.2

Write a detailed note on Structure of Probability.
07

Explain absolute and relative measure of Dispersion
07
OR

A public interest group was planning to make a court challenge to auto price rates in one of three cities: Ahmedabad, Baroda or Surat. The probability that it would choose Ahmedabad is 0.40; Baroda, 0.35; and Surat, 0.25. The group also new that it had a 60% chance of a favorable ruling if it chose Baroda, 45% if it chose Ahmedabad, and 35% if it chose Surat. If the group did receive a favorable ruling, then use the Bayes' theorem to determine which city did it most likely choose?
07
Q.3

Explain various techniques of Sampling
07

Write a detailed note on reason for Sampling.
07
2
OR
Q.3

The client company data from the Decision Dilemma reveal that 155 employees worked one of four types of positions. Shown here again is the raw values matrix
(Also called a contingency table) with the frequency counts for each category and for subtotals and totals containing a breakdown of these employees by type of position and by sex. If an employee of the company is selected randomly, what is the probability that the employee is female or a professional worker?
Type of Position
Sex
Male
Female
Managerial
8
3
Professional
31
13
Technical
52
17
Clerical
9
22
07

What is the probability of obtaining a score greater than 700 on a GMAT test that has a mean of 494 and a standard deviation of 100? Assume GMAT scores are normally distributed.
07
Q.4

The following data are the average weekly mortgage interest rates for a 40-week period. Construct a frequency distribution for these data. Calculate and display the class midpoints, relative frequencies, and cumulative frequencies for this frequency distribution.
7.29
7.23
7.11
6.78
7.47
6.69
6.77
6.57
6.80
6.88
6.98
7.16
7.30
7.24
7.16
7.03
6.90
7.16
7.40
7.05
7.28
7.30
6.87
7.68
7.03
7.17
6.78
7.08
7.12
7.31
7.40
6.35
6.96
7.29
7.16
6.97
6.96
7.02
7.13
6.84
07

According to the National Association of Insurance Commissioners, the average annual cost for automobile insurance in the United States in a recent year was $691. Suppose automobile insurance costs are uniformly distributed in the United States with a range of from $200 to $1,182. What is the standard deviation of this uniform distribution? What is the height of the distribution? What is the probability that a person's annual cost for automobile insurance in the United States is between $410 and
07
OR
Q.4

Explain how statistics is helpful in business with proper examples.
07
3
Q.4

During one holiday season, the Texas lottery played a game called the Stocking Stuffer. With this game, total instant winnings of $34.8 million were available in
70 million tickets, with ticket prizes ranging from to $1,000. Shown here are the various prizes and the probability of winning each prize. Use these data to compute the expected value of the game, the variance of the game, and the standard deviation of the game.
Prize
Probability P
1000
0.00002
100
0.00063
20
0.004
10
0.00601
4
0.02403
2
0.08877
1
0.10479
0
0.77175
07
Q.5

Use the following data for parts through
X
5
7
3
16
12
9
Y
8
9
11
27
15
13
a. Determine Correlation between two variables.
b. Determine the equation of the least squares regression line to predict y by x.
14
OR
Q.5

Explain Uniform Distribution with example.
07

Explain Exponential Distribution with example.
07