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  No. of printed pages: 2 SARDAR PATEL UNIVERSITY BBA (III Sem.) (Gen.) Examination Monday, 10 December 2012 2.30 - 4.30 pm UM03CBBA06 - Statistics for Management I Total Marks: 60
  
  Note: Figures to the right indicate full marks. Q.1 (a) Write the types of data, with their sources and write any one of the [07] source in detail. (b) For the following data, it is known that M=44 and N=100. [08] Class 10-20 5 20-30 12 30-40 ? 40-50 30 50-60 ? 60-70 10 70-80 4
  
  Find the missing frequencies and hence obtain Mean and Mode. OR Q.1 (a) Find Median, Quartile Deviation D4, P50 and P77 for following: Class 10-19 2 20-29 9 30-39 15 40-49 14 50-59 10 [08]
  
  (b) From the following prices of shares A and B, state which share is more [07] stable? Why?
  A B 55 108 54 107 52 105 53 105 56 106 58 107 52 104 50 103 51 104 49 101
  
  Q.2 (a) Define the terms: Sample space, Mutually Exclusive Events, Exhaustive Events and Complementary Event. (b) There are 6 black and some white balls in an urn. The probability of drawing 2 black balls from it is 1/3. Find the number of white balls in an urn. (c) Find the probability of 53 Sundays in a leap year. OR Q.2 (a) State and prove: (1) Addition theorem of probability (2) Multiplication theorem of probability (b) If A, B and C are three mutually exclusive and exhaustive events and if 3P(A) = 2P(B) = 6P(C); then find (1) P(AB) (2) P(BC) (3) P(AC)
  
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  Q.3 (a) Write the properties and uses of Normal distribution. (b) Between the hours of 2 and 4 p.m. the average number of phone calls per minute coming into the switch board of a company is 2.5. Find the probabilities that during one particular minute there will be (1) No phone call at all (2) Exactly 3 calls. (e-2.5 = 0.0821) (c) The probability that a bomb dropped from a plane will hit a target is 2/5. Two bombs are enough to destroy a bridge. If 4 bombs are dropped on a bridge. Find the probabilities that (1) The bridge will be saved (2) The bridge will be partially destroyed (3) The bridge will be destroyed. OR Q.3 (a) In a normal distribution 31% of the observations are less than 45 and 8% are more than 64. Find mean and standard deviation of the distribution. (b) For a Poisson variate P(1) = P(2). Find the value of P(0). (c) For a Binomial variate n=10 and P(x=5) = 2P(x=4). Find the value of P.
  
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  Q.4 (a) Give the difference between the Charts for Variable and Chart for Attributes. [05] (b) From a pharmaceutical company samples of 400 bottles were taken [05] daily for 15 days. The number of defective seals in these bottles is given below.
  ,
  
  Date Defective Seals
  
  1 28
  
  2 18
  
  3 40
  
  4 42
  
  5 32
  
  6 62
  
  7 50
  
  8 10
  
  9 30
  
  10 22
  
  11 80
  
  12 62
  
  13 76
  
  14 56
  
  15 30
  
  Draw P-chart and state your conclusion. (c) The number of defects noticed in 20 cloth pieces are given below: [05] 1, 4, 3, 2, 5, 4, 6, 7, 2, 3, 2, 5, 7, 6, 4, 5, 2, 1, 3, 8. Decide whether the process is in a State of Statistical Control. OR Q.4 (a) The following table gives the information regarding life hours of 5 lamps of [07] 10 different samples.
  ,
  
  Sample
  
  X
  R
  ,
  
  1 3290 360
  
  2 3180 210
  
  3 3350 50
  
  4 3370 100
  
  5 3280 50
  
  6 3240 400
  
  7 3260 500
  
  8 3410 200
  
  9 3310 300
  
  10 3510 600
  
  [For n=5, A2=0.58, D3=0, D4=2.11] Draw X and R charts and state your conclusions. Also give the revised limits for the control of future production. (b) Write the uses of Statistical Quality Control. [03] (c) Samples each of 250 radios are inspected for 12 days. The number of [05] defective radios found in different samples is given below. 1 2 3 4 5 6 7 8 9 10 11 12 Sample 25 47 23 30 24 34 39 32 35 22 45 40 No. of Defective Radios Prepare np-chart and state your conclusion.
  
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