Math topic中文

Finding relationship

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

Practice questions

  1. 1The owner of Eng Choo Farm claims that the eggs produced at his farm has an average cholesterol content of μ0\mu_0 mg pe…
  2. 2In this question you should state the parameters of any distributions that you use. Crispy Cream Donut Shop sells 2 type…
  3. 3XX is a normal random variable with mean 1 and variance 1, and YY is also a normal random variable with mean μ\mu and…
  4. 4Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  5. 5In this question, you should state clearly all the distributions that you use, together with the values of the appropria…
  6. 6Each 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…
  7. 7S 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…
  8. 8Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  9. 9In this question you should clearly state the values of the appropriate parameters of any distributions used. The diamet…
  10. 10The mass, XX grams, of soup packed into a can by machine AA is normally distributed with mean μ\mu grams and standard…
  11. 11The 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)…
  12. 12An automatic dispensing machine is set to dispense hot chocolate into cups. Based on observations over a long period of…
  13. 13A nursery supplies plants to Evergreen Pte. Ltd. The heights, in centimetres, of plants supplied may be taken to follow…
  14. 14[For this question, you should state clearly the values of the parameters of any normal distribution you use.] After din…
  15. 15Historical data shows that the number of goals scored per match at European Football Championships has a mean of 1.93 an…
  16. 16The masses, in grams, of the packets of semolina flour follow the distribution N(225,  252)N(225,\;25^2) and the masses, in grams,…
  17. 17A factory produces rectangular white marble floor tiles. The length of the floor tiles in centimetres can be regarded as…
  18. 18In this question you should state clearly the parameters of any normal distributions you use. The masses in kilograms of…
  19. 19At a department store, shoppers who spend more than $1000 in a single receipt are entitled to a free gift. Each shopper…
  20. 20The random variable XX has distribution N(μ,σ2)\mathrm{N}(\mu, \sigma^2). Given that P(X>k)=0.45\mathrm{P}(X > k) = 0.45, find the va…
  21. 21The continuous random variable YY has the distribution N(μ,σ2)\mathrm{N}(\mu, \sigma^2). It is known that P(Y<−a)=P(Y>5a)=0.1\mathrm{P}(Y < -a) = \mathrm{P}(Y > 5a) = 0.1…
  22. 22In this question you should state the parameters of any distribution you use. A customer service call centre categor…
  23. 23During the Great Mega Sale, the waiting times, in minutes, for men and women, at their respective fitting rooms, have me…
  24. 24Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  25. 25In this question, you should state the parameters of any distribution that you use. A local fish market is famous for tw…
  26. 26**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  27. 27The 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)…
  28. 28In this question, you should state clearly the distribution of any random variables that you define. The volume, SS, in…
  29. 29In this question you should state the parameters of any normal distributions that you use. A petrol station (Station AA…
  30. 30The finishing times in a 10km race with a large number of runners follow a normal distribution. After 40 minutes, 10% of…
  31. 31In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
  32. 32A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  33. 33In this question you should state clearly all the distributions that you use, together with the values of the appropriat…
  34. 34**In this question you should state clearly all the distributions that you use, together with the values of the appropri…
  35. 35Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes – Regular-sized packets an…
  36. 36Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  37. 37In a Junior College, the Physical Education (PE) department is analyzing the running time taken by girls from 2 cohorts,…
  38. 38The waiting time for a patient to see a doctor in a clinic is TT minutes. The waiting times of a randomly chosen sample…
  39. 39The speeds of an e-scooter (XX km/h) and a pedestrian (YY km/h) measured on a particular stretch of footpath are norma…
  40. 40In this question you should state the parameters of any distributions that you use. To regulate the use of its facil…
  41. 41Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  42. 42Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  43. 43In an examination, the score, XX, for paper 1 of a student is found to follow a normal distribution with mean 62 and st…
  44. 44A sample of nn observations was taken from a population of mean μ\mu and variance 10. Find the least sample size requi…
  45. 45In this question you should state clearly the values of the parameters of any normal distributions you use. A fruit…
  46. 46In this question you should state the parameters of any distributions you use. A snack company produces two types of…
  47. 47In this question you should state the parameters of any distributions that you use. To regulate the use of its facilitie…
  48. 48The table below shows the BMI-for-age for boys aged 18 years in Singapore. | Age (years) | Weight Indicator | Underweigh…
  49. 49Fruits are sold by weight. Apples are sold at $2 per kg and oranges at $3 per kg. The masses, in kg, of apples and ora…