Math topic中文

Central limit theorem

Use of the Central Limit Theorem to treat sample mean as having normal distribution when the sample size is sufficiently large (e.g. n≥30n\ge 30).

Practice questions

  1. 1A bakery claims that the mass of a cake, on average, is 600 grams each. A random sample of 10 cakes is examined and the…
  2. 2Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  3. 3Researchers at University S claimed that Fungus A, a strain of fungi that is typically found in soil and plants, was a…
  4. 4S and T are independent random variables with the distributions N(18,32)N(18,3^2) and N(μ,σ2)N(\mu,\sigma^2) respectively. It is gi…
  5. 5The waiting time for a patient to see a doctor in a clinic is TT minutes. The waiting times of a randomly chosen sample…
  6. 6Energy bars are a convenient source of nutrition for athletes. A typical energy bar weighs between 30-50 g and is likely…
  7. 7Section B: Probability and Statistics [35 marks] From past data, it is known that the mean time taken by students at…
  8. 8**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  9. 9In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieties,…
  10. 10Packets of a particular brand of potato chips are delivered to a supermarket in boxes of 60. On average, 1.8 packets in…
  11. 11The probability of obtaining a head when a particular coin is tossed is pp. A fair cubical die has the number '1' on on…
  12. 12A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  13. 13A manufacturer claims that the mean lifetime of the light bulbs he produces is at least 1200 hours. A random sample of 1…
  14. 14An automatic dispensing machine is set to dispense hot chocolate into cups. Based on observations over a long period of…
  15. 15Historical data shows that the number of goals scored per match at European Football Championships has a mean of 1.93 an…
  16. 16In a laboratory, the time in minutes for an inspector to test an electrical circuit board is a continuous random variabl…
  17. 17The production manager of a badminton racket company wishes to check that the mean mass of the badminton rackets produce…
  18. 18Green Earth Factory produces solar panels. On average, 2% of the solar panels produced are found to contain defects. The…
  19. 19A company produces reinforcing bars for use in construction. The production manager claims that the mean tensile strengt…
  20. 20Alice uses a computer program to simulate 80 tosses of a biased coin. Let YY be the random variable denoting the number…
  21. 21During the Great Mega Sale, the waiting times, in minutes, for men and women, at their respective fitting rooms, have me…
  22. 22EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
  23. 23Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  24. 24The amount customers spend is often correlated with the amount of time they spend in stores. According to a national sur…
  25. 25A hand sanitiser company, Cleanser, claims that the mean volume of each bottle of their hand sanitiser is 15 ml. The con…
  26. 26Based on observations over a long period, the mean time taken by male students in Griffles Junior College (GJC) to compl…
  27. 27A factory manufactures a large number of chips in a variety of colours and packs them into boxes. Each box contains 36 r…
  28. 28A 6-sided die has three faces marked with a '1', two faces marked with a '2' and one face marked with a '3'. Another 6-s…
  29. 29A factory produces sausage rolls of length 10 cm. The production manager wishes to take a random sample of sausage rolls…
  30. 30In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
  31. 31EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
  32. 32A firm claims that, on average, their workers spend no more than 8 hours a day at the construction site. The amount of t…
  33. 33A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  34. 34A researcher is running a trial of a new variety of potato. A field contains 20 rows of the new variety of potato plants…
  35. 35Good Papa Caf'e sells only two types of muffins, chocolate and banana. The number of chocolate and the number of banana…
  36. 36Flour is packed in bags of 1.5 kg, as stated on the packaging, by two separate machines A and B in a factory. During a q…
  37. 37**In this question you should state clearly all the distributions that you use, together with the values of the appropri…
  38. 38Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes – Regular-sized packets an…
  39. 39In a box of cheese rings from a certain manufacturer, the mass of sodium, XX mg, is a continuous random variable with m…
  40. 40Eastham is a football club in a competitive league. It is found that the average time taken by Eastham to score their fi…
  41. 41The waiting time for a patient to see a doctor in a clinic is TT minutes. The waiting times of a randomly chosen sample…
  42. 42In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieti…
  43. 43Tim is a student in a school with a large student population. As part of his project, Tim would like to interview some o…
  44. 44In a game, a player selects one ball at random from a bag which contains four balls numbered '1', '1', '2' and '3'. The…
  45. 45One round of a game is played by randomly moving the counter from the starting point XX to one of the ending points AA…
  46. 46Over a period of one month, the increase in heights of orchid plants in a nursery has mean 1.34 cm and standard deviatio…
  47. 47Every morning, Peter has to take a bus to school. On average, he reaches the bus stop at 6:30 am each day. His arrival t…
  48. 48A supermarket sells boxes of a particular brand of biscuits in two flavours, chocolate and strawberry. The mean number o…
  49. 49A particular streaming service platform claims that the average time a user spends watching content on the platform per…
  50. 50A random sample of 27 individuals from a population of young men aged 18 was chosen and the length of the right foot of…
  51. 51In a box of cheese rings from a certain manufacturer, the mass of sodium, XX mg, is a continuous random variable with m…
  52. 52In the swimming training school AquaV, the time taken to swim a lap of the pool by the trainees is found to have a mean…
  53. 53Mr Tan, who is the school Admin Manager, believes that JC students in his school take 22 minutes on average to buy and c…