1) Construct a cumulative frequency distribution & percentage cumulative frequency distribution for the data given below pertaining to lifetime of 400 radio tubes testing.

Lifetime( hrs) No. of Tubes300-399 14400-499 46500-599 58600-699 76700-799 68800-899 62900-999 481000-1099 221100-1199 6

2) Data given below pertaining to lifetime of 400 radio tubes testing, estimate the percentage of tubes that have lifetime of (A) less than 560 hrs,(B) 970 or more hrs, (C) between 620 and 890 hrs

Lifetime( hrs) No. of Tubes300-399 14400-499 46500-599 58600-699 76700-799 68800-899 62900-999 481000-1099 221100-1199 6

3) Following table shows diameters in mm, of a sample 60 ball bearings. Construct a frequency distribution using appropriate class intervals. Also construct a cumulative frequency distribution & percentage cumulative frequency distribution

7.38 7.29 7.43 7.40 7.36 7.41 7.35 7.31 7.26 7.377.28 7.37 7.36 7.35 7.24 7.33 7.42 7.36 7.39 7.357.45 7.36 7.42 7.40 7.28 7.38 7.25 7.33 7.34 7.327.33 7.30 7.32 7.30 7.39 7.34 7.38 7.39 7.27 7.357.35 7.32 7.35 7.27 7.34 7.32 7.36 7.41 7.36 7.447.32 7.37 7.31 7.46 7.35 7.35 7.29 7.34 7.30 7.40

4) Following table shows diameters in mm, of a sample 60 ball bearings. Construct a frequency distribution using appropriate class intervals. Determine the percentage of ball bearings having diameters (a) exceeding 7.32 mm, (b) not more than 7.36 mm, (c) between 7.30 & 7.38 mm

7.38 7.29 7.43 7.40 7.36 7.41 7.35 7.31 7.26 7.377.28 7.37 7.36 7.35 7.24 7.33 7.42 7.36 7.39 7.357.45 7.36 7.42 7.40 7.28 7.38 7.25 7.33 7.34 7.327.33 7.30 7.32 7.30 7.39 7.34 7.38 7.39 7.27 7.357.35 7.32 7.35 7.27 7.34 7.32 7.36 7.41 7.36 7.447.32 7.37 7.31 7.46 7.35 7.35 7.29 7.34 7.30 7.40

5) Total number of farms and respective sales figures are tabulated below, total no. of farms are 1945000. From this determine the number of farms in which sales (a) exceeded 40000, (b) were less than 40000, (c) were between 30000 & 50000

Sales Farms (percent)Under 2500 25.92500-4999 13.25000-9999 13.010000-19999 11.720000-39999 11.040000--99999 14.4100000-249000 8.5250000-499999 1.8500000 and over 0.6

6) Find Mean, Median & mode for the following distribution , maximum loads in kilonewtons supported by certain cables

Maximum load (Kn) Number of cables93-97 298-102 5103-107 12108-112 17113-117 14118-122 6123-127 3128-132 1

7) Find Mean, Median & mode for the following distribution, diameter of rivet manufactured by a company.

Diameter ( mm) frequency7.247-7.249 27.250-7.252 67.253-7.255 87.256-7.258 157.259-7.261 427.262-7.264 687.265-7.267 497.268-7.270 257.271-7.273 187.274-7.276 127.277-7.279 47.280-7.282 1

8) Find Mean, Median & mode for the following distribution Class Frequency10 to under 15 315 to under 20 720 to under 25 1625 to under 30 1230 to under 35 935 to under 40 540 to under 45 2

9) Find Mean, Median & mode for the following distribution

Age (years) Male( '000) Female( '000)18-21 121 48122-25 2441 418426-29 5930 695230-33 6587 719334-37 11788 1189338-41 9049 902242-45 8749 817146-49 5786 465450-53 2581 1524

10) Find Mean, Median & mode for the following distribution, Grade No. of students90-100 980-89 3270-79 4360-69 2150-59 1140-49 330-39 1

11) Find Mean deviation and standard deviation for the following distribution , maximum loads in kilonewtons supported by certain cables.

Maximum load (Kn) Number of cables93-97 298-102 5103-107 12108-112 17113-117 14118-122 6123-127 3128-132 1

12) Find Mean deviation & standard deviation for the following distribution Class Frequency10 to under 15 315 to under 20 720 to under 25 1625 to under 30 1230 to under 35 935 to under 40 540 to under 45 2

13) Find Mean deviation & standard deviation for the following distribution standard deviation Grade No. of students90-99 980-89 3270-79 4360-69 2150-59 1140-49 330-39 1

14) Find Mean deviation & standard deviation for the following distributionAge (years) Male( '000) Female( '000)18-21 121 48122-25 2441 418426-29 5930 695230-33 6587 719334-37 11788 1189338-41 9049 902242-45 8749 817146-49 5786 465450-53 2581 1524

15) Find Mean deviation & standard deviation for the following distributionDiameter ( mm) frequency7.247-7.249 27.250-7.252 67.253-7.255 87.256-7.258 157.259-7.261 427.262-7.264 687.265-7.267 497.268-7.270 257.271-7.273 187.274-7.276 127.277-7.279 47.280-7.282 1

16) Determine probability thata) A king, ace, jack of clubs or queen of diamonds appear in drawing a single card from a well-

shuffled pack of 52 cards. b) A marble is drawn at random from a box containing 10 red, 30 white, 20 blue & 15 orange

marbles, the marble drawn is orange or red c) 2 marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue & 15 orange

marbles and replacement is made after each draw, both are whited) 2 cards are drawn successively from pack of well shuffled pack of 52 cards, first card is not a

club 10 or an ace17) Determine probability that

a) the sum 8 appears in a single toss of a pair of fair diceb) A marble is drawn at random from a box containing 10 red, 30 white, 20 blue & 15 orange

marbles, the marble drawn is not red or bluec) 2 marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue & 15 orange

marbles and replacement is made after each draw, first is red and second is whited) 2 cards are drawn successively from pack of well shuffled pack of 52 cards, first card is an ace

but second is not18) Determine probability that

a) A non defective bolt will be found if out of 600 bolts already examined, 12 were defectiveb) A ball is drawn at random from a box containing 10 red, 30 white, 20 blue & 15 orange balls,

the ball drawn is not blue

c) 2 marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue & 15 orange marbles and replacement is made after each draw, neither is orange

d) 2 cards are drawn successively from pack of well shuffled pack of 52 cards, at least one card is diamond

19) Determine probability that a) 7 or 11 comes up in a single toss of a pair of fair diceb) A ball is drawn at random from a box containing 10 red, 30 white, 20 blue & 15 orange balls,

the ball drawn is whitec) 2 marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue & 15 orange

marbles and replacement is made after each draw, second is not blue.d) 2 cards are drawn successively from pack of well shuffled pack of 52 cards, Cards are not of

same suite20) Determine probability that

a) at least one head appears in three tosses of a fair coinb) A ball is drawn at random from a box containing 10 red, 30 white, 20 blue & 15 orange balls,

the ball drawn is white, blue or red c) 2 marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue & 15 orange

marbles and replacement is made after each draw, at least one is blued) 2 cards are drawn successively from pack of well shuffled pack of 52 cards, not more than one

card is a picture card21) a) Find the probability that in tossing fair coin 6 times, the head will appear 0 times b) An insurance sales person sells policies to 5 men, all of identical age & in good health. According to actuarial tables, the probability that a man of his particular age will be alive 30 years hence is 2/3. Find probability that in 30 years at least 3 men will be alive c) Between 2 to 4 p.m. average number of phone calls per minute coming into the switchboard of a company is 2.5, find the probability that during one particular minute there will be 0 calls d) If the weight of 300 students, are normally distributed with mean of 66 kg and standard deviation of 3 kg, how many students have weights greater than 70 kg e)If the diameters of ball bearings are normally distributed with mean 6.14 mm and standard deviation 0.025 mm, determine percentage of ball bearings with diameters between 6.10 to 6.18 mm( both inclusive)

22) a) Find the probability that in tossing fair coin 6 times, the head will appear 1 times b) an insurance sales person sells policies to 5 men, all of identical age & in good health. According to actuarial tables, the probability that a man of his particular age will be alive 30 years hence is 2/3. Find probability that in 30 years all 5 men will be alive c) Between 2 to 4 p.m. average number of phone calls per minute coming into the switchboard of a company is 2.5, find the probability that during one particular minute there will be 1 calls d) If the weight of 300 students, are normally distributed with mean of 66 kg and standard deviation of 3 kg, how many students have weights less than or equal to 62 kg e) If the diameters of ball bearings are normally distributed with mean 6.14 mm and standard deviation 0.025 mm, determine percentage of ball bearings with diameters greater than 6.17 mm

23) a) Find the probability that in tossing fair coin 6 times, the head will appear 2 times b) an insurance sales person sells policies to 5 men, all of identical age & in good health. According to actuarial tables, the probability that a man of his particular age will be alive 30 years hence is 2/3. Find probability that in 30 years only 2 men will be alive c) Between 2 to 4 p.m. average number of phone calls per minute coming into the switchboard of a company is 2.5, find the probability that during one particular minute there will be 2 calls

d) If the weight of 300 students, are normally distributed with mean of 66 kg and standard deviation of 3 kg, how many students have weights between 63 & 69 kg ( both inclusive)

e) If the diameters of ball bearings are normally distributed with mean 6.14 mm and standard deviation 0.025 mm, determine percentage of ball bearings with diameters less than 6.08 mm

24) a) Find the probability that in tossing fair coin 6 times, the head will appear 3 times b) an insurance sales person sells policies to 5 men, all of identical age & in good health. According to actuarial tables, the probability that a man of his particular age will be alive 30 years hence is 2/3. Find probability that in 30 years at least 1 man will be alive c) Between 2 to 4 p.m. average number of phone calls per minute coming into the switchboard of a company is 2.5, find the probability that during one particular minute there will be 3 calls d) If the weight of 300 students, are normally distributed with mean of 66 kg and standard deviation of 3 kg, how many students have weights equal to 66 kg e) If the diameters of ball bearings are normally distributed with mean 6.14 mm and standard deviation 0.025 mm, determine percentage of ball bearings with diameters equal to 6.15 mm

25) a) Find the probability that in tossing fair coin 6 times, the head will appear 4 times b) an insurance sales person sells policies to 5 men, all of identical age & in good health. According to actuarial tables, the probability that a man of his particular age will be alive 30 years hence is 2/3. Find probability that in 30 years none of the men will be alive c) Between 2 to 4 p.m. average number of phone calls per minute coming into the switchboard of a company is 2.5, find the probability that during one particular minute there will be 4 or fewer calls d) If the weight of 300 students, are normally distributed with mean of 66 kg and standard deviation of 3 kg, how many students have weights less than 65 kg

e) If the diameters of ball bearings are normally distributed with mean 6.14 mm & standard deviation 0.025 mm, determine percentage of ball bearings with diameters greater than or equal to 6.165 mm

26) why is it true that classes in frequency distributions are all-inclusivea) no data point falls into more than one classb) every class has a class markc) all data fit into one class or anotherd) all the abovee) a & c but not b

27) when constructing a frequency distribution, the first step isa) calculate the class marks for the datab) sort the data points into classes and count the number of points in each class c) decide on type and number of classes for dividing the datad) none of the above

28)which of the following statements is true about cumulative frequency olive for a particular set of data

a) both "more than" & " less than" curves have the same slopeb) "more than" curves slope up and to the rightc) " less than" curves slope down and to the rightd) " less than" curves slope up and to the right

29) if data can take on only a limited number of values, the classes of these data are called --------------- ,otherwise, the classes are called ---------------.30) a ----------------- is a collection of all the elements in a group . a collection of some , but not all, of these elements is a --------------.

31) what is the major assumption we make when computing a mean from a grouped dataa) all values are discreteb) every value in a class is equal to class markc) no values occurs more than onced) each class contains exactly the same number of values

32)which of the following statements is NOT correcta) some data sets do not have meansb) calculation of a mean is affected by extreme data valuesc) a weighted mean should be used when it is necessary to take the importance of each value into

accountd) all these statements are correct

32) which of the following is NOT an advantage of using a mediana) extreme values affect median less strongly than they do the meanb) a median can be calculated for qualitative descriptionsc) the median can be calculated for every set of data, even for all sets containing open ended

classesd) the median is easy to understand

33) why it is usually better to calculate a mode from grouped, rather than ungrouped, dataa) the ungrouped data tends to be bimodalb) mode for grouped data will be the same, regardless of the skewnes of the distributionc) extreme values have less effect on grouped datad) the chance of an unrepresentative value being chosen as the mode, is reduced

34) in which of these cases would the mode be most useful as an indicator of central tendencya) every value in the data set occurs exactly onceb) all but three values in a data set occur once, 3 values occur 100 times eachc) all values in a data set occur 100 times eachd) every observation in a data set has the same value

35) why is it necessary to square the differences from the mean when computing the variancea) so that extreme values will not affect the calculationb) because it is possible that N could be very smallc) some of the differences will be positive & some will be negatived) none of these

36) assume that a population has Mean = 100 ,standard deviation = 10 & N = 1000. According to chebyshev's theorem, which of the following situation is NOT possible

a) 150 values are greater than 130b) 930 values lie between 100 & 108c) 22 values lie between 120 & 125d) 90 values are less than 70

37) which of the following is an example of relative measure of dispersiona) standard deviationb) variancec) coefficient of variationd) all of the above

38) which of the following is truea) variance can be calculated for grouped or ungrouped datab) standard deviation can be calculated grouped or ungrouped datac) standard deviation can be calculated grouped or ungrouped data, but variance can be calculated

only for grouped datad) a & b but not c

39) the measure of average squared distance between the mean & each item in the population is the ------------------, the positive square root of this value is the --------------40) what is the probability that a value chosen at random from a particular population is larger than the median of the population

a) 0.25 b) 0.5 c) 1.0 d) 0.6741) assume that a single fair dice is rolled once which of the following is true.

a) the probability of rolling a number higher than 1 is 1 - P(one is rolled)b) the probability of rolling a 3 is 1 - P ( 1,2,4,5or 6 is rolled)c) the probability of rolling a 5 or 6 is higher than the probability of rolling 3 or 4d) all of thesee) a & b but not c

42) a taxi driver in Mumbai ahs found that the weather affects his customers' tipping. If it is raining his customers usually tip poorly. When it is not raining, however, they usually tip well. Which of the following is true.

a) tips and weather are statistically independentb) tips & weather conditions are not mutually exclusivec) P ( good tip/ rain) is larger than P( bad tip/ rain)d) None of thesee) A & c but not b

43) one of the possible outcomes of doing something is a -------------. The activity that produced this outcome is a ----------------

44) let G be event that a girl is born, Let F be event that a baby over 8 pounds is born. Characterize the union of events & intersection of events using Venn diagram & symbolically

45) a die is tossed twice, 2 outcomes are noted , draw a Venn diagram of sample space & indicate the event" second toss is greater than the first, calculate the probability of the event-

46) brokerage firm deals with stocks & bonds, Analyst for the firm is interested in assessing probability that a person who inquires about the firm will eventually purchase stock or bonds, also find union & intersection of events using Venn diagram & symbolically

47) you draw a card from standard pack of 52 cards & keep it face down without looking at it. Your friend then picks up a card at random from remaining cardsa) what is the probability that your card is ace of spade b) what is the probability that friends card is ace of spadec) you turn over your card & it is 10 of diamonds, now what is the probability that your friends card

is ace of spade?

48) machine produces components for use in cellphone. At any given time machine may be in one of the 3 states Operational, Out Of Control, Down (under maintenance). From past experience, it is known that probability that machine is out of order at any moment is 2% & that it is down is 1.5%.a) what is the relationship between the 2 events- - machine out of control & machine downb) when machine is out of control or down a mechanic must be called, what is the probability that

mechanic must be called right now? c) unless machine is down, it can be used to produce single item , what is the probability that

machine can be used to produce single item now?

49) as part of MET annual event, students project was undertaken in which 28 horses were made to listen to Pt. Ravishankar & Lata Mangeshkar. Results were- 11 out of 28 horses exhibited some head movement when Ravishankar's music was played & 8 exhibited some head movement when Lata's songs were played. 5 horses moved their heads when music of both the stalwarts was played. If a horse is chosen at random what is the probability that horse exhibits head movements to Pt Ravishankar's music or Lata Mangeshkar's songs or to both?

50) 21.5% of executives in HLL are at top salary level, 40% of all executives at HLL are woman. 6.4% of all executives are woman & are at top salary level. Whether there is any evidence of salary inequality, what is your opinion?51) Projected probability of increase in online sales (E-commerce) from year 2004 to 2005 is 95% in USA, 90% in Australia, 85 % in Japan. What is the probability that online sales will increase in all 3 countries?

52)21.5 of executives in Lintas are at top salary level, 40% of all executives at lintas are woman. 6.4% of all executives are woman & are top salary level. Whether there is any evidence of salary inequality, what is your opinion ? 53) a large competitor will buy a small firm, firms stock price will rise with .85 probability. The purchase of the firm has 0.4 probability. What is the probability that purchase of small firm will take place & firms stock will rise? 0.3454)number of claims in large insurance company are categorized by kind & region

East South North WestHospitalization 75 128 29 52Physician's visit 233 514 104 251Outpatient treatment 100 326 65 99

A bill is chosen at random what is the probability thata) it is from north - b) it is from east -c) it is either from north or south - d) is for hospitalization- e) given that bill is for hospitalization probability it is from south - f) given that bill is from south probability it is for physician's visit - g) given that bill is for outpatient treatment probability it is from west - h) it is from east or for outpatient treatment - i) it is for hospitalization or from south 55)an investment analyst collects data on stocks & about payment of dividend & change in stock prices over a period

price increase no increase in pricedividend paid 34 78no dividend paid 85 49 if stock is selected at random find the probability thata) price increased - b) paid dividend - c) price increased as well as dividend paid - d) neither price increased nor dividend was paid - e) given that stock prices increased, probability that dividend also was paid -f) given that dividend was not paid, probability that price increased - g) was the stock worth holding during the period in question ? -

1)a faculty member is applying for a new position chancellor of university in 7 universities, in 3 universities he is a finalist( he is among 3 short-listed), in 2 universities he is one of the 6 short-listed, in 2 universities he is in early stage of application screening in pool of 200 applicants. Assuming that there is no exchange of information, influence across universities about hiring decision , what is the probability that faculty gets at least one job offer for chancellor post - 0.81432)projected probability of increase in online sales ( E-commerce) from year 2004 to 2005 is 95% in USA, 90% in Australia, 85 % in Japan. What is the probability that online sales will increase in all 3 countries -

1)a test is administered on ill person, test will indicate so with probability of 92%, when administered to a person who is not ill, test will erroneously give a positive result with a probability 0.04, suppose illness is rare & is known to affect only 0.1% of population, if a person is randomly selected from population & is given a test & result in positive, what is the probability that person is ill? 2) when economic situation is high certain economic indicator rises with probability 0.6 when economic situation is medium certain economic indicator rises with probability 0.3when economic situation is low certain economic indicator rises with probability 0.1economy is high 15% of time, medium 70% , low 15%. Given that indicator has just gone up , what is the probability that economy is high- 3) in a test marketing of a product test will indicate success75% time when it is indeed successful & 15% of time when it is not successful. New product has 60% chance of success. If test indicates that product will be successful what is the probability that it is really successful - 4) 2 stocks A & P from same industry, are known to be related, probability that A will go up tomorrow is 0.2 & that both go up is 0.12. suppose that tomorrow you find that A goes up what is the probability that B goes up as well- 5) a financial service company advertises in magazines, runs bill board ads & on television. Co estimates that individual seeing the billboard = 0.1, magazine = 0.15, television = 0.2 probability. What is the probability that randomly selected person will be exposed to at least one method of advertising = 6) company internal accounting standards as set, ensure that no more than 5% accounts are in error. A random sample of accounts are collected to see how many are in error. The error rate is indeed 5% and 10% accounts are chosen at random. What is the probability that none will be in error7) in MET 30% students are from MMM, 35% MFM, 20% HR, 15% IM from past records it is known that 20% MMM students fail in statistics exam, whereas failure % for MFM is 30% , MHRDM is 35% & MIM is 40% . given that a student has failed in statistics, what is the probability that student is from MIM-- 8) government is thinking of lowering the personal income tax rates & has appointed a committee consisting of 38 members. It requires a simple majority to pass the new legislation. If probability that each member votes "yes" is 0.25, find the probability that the legislation will be passed