Math topic中文

Finding probability

Finding the value of P(X<x1)\mathrm{P}(X<x_1) or a related probability, given the values of x1x_1, μ\mu, σ\sigma.

Practice questions

  1. 1Section B: Statistics [60 marks] A manager claims that the time spent by each customer at his supermarket follows a norm…
  2. 2In this question you should state the parameters of any distributions that you use. Crispy Cream Donut Shop sells 2 type…
  3. 3In a standardized assessment test conducted annually, it is found that, on average, 1 in 5 students who sit for the test…
  4. 4A credit card company has a special 24-hour telephone hotline for customers to either report a lost credit card or to re…
  5. 5Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  6. 6In this question, you should state clearly all the distributions that you use, together with the values of the appropria…
  7. 7Each day a train travels from Town A to Town B and it is scheduled to arrive at Town B at 0800 hrs. During the first yea…
  8. 8S 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…
  9. 9**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  10. 10Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  11. 11In this question you should state clearly the values of the parameters of any normal distributions that you use. The mas…
  12. 12In this question you should clearly state the values of the appropriate parameters of any distributions used. The diamet…
  13. 13In each large batch of SIM cards, 15% of the cards are defective. From each batch, a random sample of 10 cards is drawn…
  14. 14The mass, XX grams, of soup packed into a can by machine AA is normally distributed with mean μ\mu grams and standard…
  15. 15A blogger observes that his blog receives an average of 3.2 visitors a day. Assuming a Poisson distribution, find the pr…
  16. 16In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieties,…
  17. 17Packets of a particular brand of potato chips are delivered to a supermarket in boxes of 60. On average, 1.8 packets in…
  18. 18The random variable XX is normally distributed with mean μ\mu and variance σ2\sigma^2. Find P(X>μ+0.05σ)\mathrm{P}(X > \mu + 0.05\sigma)…
  19. 19The probability of obtaining a head when a particular coin is tossed is pp. A fair cubical die has the number '1' on on…
  20. 20The average number of calls per hour received by telephone operators at the Call Centre of bank ECBC is being reviewed.…
  21. 21A nursery supplies plants to Evergreen Pte. Ltd. The heights, in centimetres, of plants supplied may be taken to follow…
  22. 22[For this question, you should state clearly the values of the parameters of any normal distribution you use.] After din…
  23. 23The masses, in grams, of the packets of semolina flour follow the distribution N(225,  252)N(225,\;25^2) and the masses, in grams,…
  24. 24In this question you should state clearly the parameters of any normal distributions you use. The masses in kilograms of…
  25. 25At a department store, shoppers who spend more than $1000 in a single receipt are entitled to a free gift. Each shopper…
  26. 26On a Friday evening, the class chairperson emails his 20 classmates to propose an outing to watch a newly released actio…
  27. 27To reduce the number of speeding incidents on the road, traffic police in Country S set up traffic cameras at 3 busy tra…
  28. 28A credit card company has a special 24-hour telephone hotline for customers to either report a lost credit card or to re…
  29. 29已知随机变量ξ服从标准正态分布N（0，1），若P（ξ＜-1.96）=0.025，则P（|ξ|＜1.96）= ．
  30. 30Green Earth Factory produces solar panels. On average, 2% of the solar panels produced are found to contain defects. The…
  31. 31In this question you should state the parameters of any distribution you use. A customer service call centre categor…
  32. 32Alice uses a computer program to simulate 80 tosses of a biased coin. Let YY be the random variable denoting the number…
  33. 33During the Great Mega Sale, the waiting times, in minutes, for men and women, at their respective fitting rooms, have me…
  34. 34In a school canteen, the number of people joining the noodle stall queue in a period of 30 seconds is a random variable…
  35. 35In this question, you should state the parameters of any distribution that you use. A local fish market is famous for tw…
  36. 36At the drinks stall in a canteen, both hot and cold drinks are sold. The number of hot drinks sold per minute follows a…
  37. 37**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  38. 38On a Friday evening, the class chairperson emails his 20 classmates to propose an outing to watch a newly released actio…
  39. 39The random variable XX has distribution N(μ,σ2)N(\mu,\sigma^{2}). Given that P(X>k)=0.45P(X>k)=0.45, find the value of P(X>2μ−k)P(X>2\mu - k)…
  40. 40In this question, you should state clearly the distribution of any random variables that you define. The volume, SS, in…
  41. 41In this question you should state the parameters of any normal distributions that you use. A petrol station (Station AA…
  42. 42A factory manufactures a large number of chips in a variety of colours and packs them into boxes. Each box contains 36 r…
  43. 43A 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…
  44. 44The finishing times in a 10km race with a large number of runners follow a normal distribution. After 40 minutes, 10% of…
  45. 45In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
  46. 46Good Papa Caf'e sells only two types of muffins, chocolate and banana. The number of chocolate and the number of banana…
  47. 47A factory manufactures paperweights consisting of glass mounted on a wooden base. The volume of glass, in cm3\text{cm}^3,…
  48. 48Epple Company manufactures a large number of E-phones. It is known that 1% of the E-phones manufactured are defective. A…
  49. 49In this question you should state clearly all the distributions that you use, together with the values of the appropriat…
  50. 50**In this question you should state clearly all the distributions that you use, together with the values of the appropri…
  51. 51A grocery store sells two types of apples, Brand AA and Brand SS. The masses (in grams) of the apples for each brand c…
  52. 52Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  53. 53In a Junior College, the Physical Education (PE) department is analyzing the running time taken by girls from 2 cohorts,…
  54. 54The speeds of an e-scooter (XX km/h) and a pedestrian (YY km/h) measured on a particular stretch of footpath are norma…
  55. 55In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieti…
  56. 56In this question you should state the parameters of any distributions that you use. To regulate the use of its facil…
  57. 57'Famous Amas' makes two types of cookies, almond cookie and chocolate chip cookie. The mass of an almond cookie and a ch…
  58. 58In a game, a player selects one ball at random from a bag which contains four balls numbered '1', '1', '2' and '3'. The…
  59. 59One round of a game is played by randomly moving the counter from the starting point XX to one of the ending points AA…
  60. 60It is known that 8% of the population of a large city use a particular web browser called Voyager. A researcher wishes t…