EDUTION INSTITUTE

G.C.E (A/L)

Business Statistics

Answer 5 Questions Only

Question No -01

The following grouped frequency distribution summarises the

number of minutes, to the nearest minute, that a random sample of

200 motorists were delayed by road works on a stretch of

motorway.

Delay (mins)

Number of motorists

4—6 15 7—8 28

9 49 10 53

11—12 30 13—15 15 16—20 10

(a) Give a reason to justify the use of a histogram to represent these

data. (1 mark)

(b) Estimate the median of this distribution. (2 marks)

(c) Calculate an estimate of the mean and an estimate of the

standard deviation of

these data. (5 marks)

(d) List the advantages and disadvantages of Mean and standard

deviation. (3marks)

One coefficient of skewness is given by

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P.Suthaharan BBA (Marketing Special)(Col) Duration: 2.5 Hours

Paper - 03/May/2011/HRN

(e) Evaluate this coefficient for the above data. (2 marks)

(f) Explain why the normal distribution may not be suitable to model

the

number of minutes that motorists are delayed by these

roadworks.(2marks)

Question No -02

(a) Explain briefly what you understand by (i) a statistical experiment (1) (ii) an event. (2)

(b) State one advantage and one disadvantage of a statistical model. (2)(c) Briefly explain the concept of Beye’s Theorem (4)(d) A discrete random variable X has the probability function shown in

the table below.

(I) Given that E(X) = 5/6, find a. (3)

(II) Find the exact value of Var (X). (3)

Question No -03.

1. Briefly explain why measures of dispersion/deviation are important? (3 marks)

2. Following data shows the age distribution of patients getting treatment in a hospital. By using central tendency measures find out the coefficient of skewness and explain the result.

58,39,30,48,27,16,56,56,65,63(5 marks)

3. In a resent survey, the following usage patterns of refrigerators were identified.

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Usage(years) No of No ofRefrigirators Refrigiratorstype A type B

0-2 5 22-4 16 74-6 13 126-8 7 19

8-10 5 910-12 4 1

1. Which type of refrigerators having highest usage2. If the prizes of both refrigerators are same, which refrigerator would you

recommend to a rational buyer? (7marks)

Question No -04

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Question No -05

I. Explain what is mean by total probability rule and prove it (5)

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II. A contractor bids for two building projects. He estimates that the

probability of winning the first project is 0.5, the probability of

winning the second is 0.3 and the probability of winning both projects

is 0.2.

(a) Find the probability that he does not win either project. (3)

(b) Find the probability that he wins exactly one project. (2)

(c) Given that he does not win the first project, find the

probability that he wins the second. (2)

(d) By calculation, determine whether or not winning the first

contract and winning the second contract are independent

events. (3)

Question No -06

1. Compare and contrast ‘the simple event’ and the compound event with the support of an example (3 marks)2. Define ‘independent event’ and prove, if event A,B are independent the complementary events of A and B also independent. (4 marks)

3. Prove each of the statements below are wrong.I. If two events are exhaustive, P (A) =1/4 , P (B) = 1/3 and P (AuB) = ¾

II. In a road, the probability for exactly one accident 0.23. Probability for at least one accident 0.18 (3 marks)

4. You are given following information regarding a bag containing 11 bulbs, you have been asked to choose a bulb from that bag.

60W 100W TotalBugs -error 3 3 6de-bugs -No error 2 3 5

1. The probability of the bulb chosen is defective?2. If the Bulb chosen is 60W, What is the probability that is a bug

defective bulb.(5 marks)

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Question No -07

1. Define different type of random variable and support your answer with example. (3 marks)2. What is your understanding of the term ‘probability distribution’

(2 marks)3. List down the conditions that should be fulfilled by a probability distribution (4 marks)4. Random variable ‘x’ has following probability distribution.

i. Find the value of Kii. P(X ≤ 3)iii. P(2 ≤ X ≤ 3)

(4 marks)

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X 1 2 3 4

P(X) 1/3 1/3 k 1/4