Math topic中文

Standard normal

Standard normal distribution.

Practice questions

  1. 1Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  2. 2XX is a normal random variable with mean 1 and variance 1, and YY is also a normal random variable with mean μ\mu and…
  3. 3Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  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 clearly state the values of the appropriate parameters of any distributions used. The diamet…
  6. 6During training, the time in seconds for a soldier to dismantle a certain type of equipment is a normally distributed co…
  7. 7The mass, XX grams, of soup packed into a can by machine AA is normally distributed with mean μ\mu grams and standard…
  8. 8The 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)…
  9. 9An automatic dispensing machine is set to dispense hot chocolate into cups. Based on observations over a long period of…
  10. 10A nursery supplies plants to Evergreen Pte. Ltd. The heights, in centimetres, of plants supplied may be taken to follow…
  11. 11A factory produces rectangular white marble floor tiles. The length of the floor tiles in centimetres can be regarded as…
  12. 12In this question you should state clearly the parameters of any normal distributions you use. The masses in kilograms of…
  13. 13The 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…
  14. 14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）= ．
  15. 15Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  16. 16In a school canteen, the number of people joining the noodle stall queue in a period of 30 seconds is a random variable…
  17. 17In this question, you should state the parameters of any distribution that you use. A local fish market is famous for tw…
  18. 18The 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)…
  19. 19In this question, you should state clearly the distribution of any random variables that you define. The volume, SS, in…
  20. 20In this question you should state the parameters of any normal distributions that you use. A petrol station (Station AA…
  21. 21In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
  22. 22A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  23. 23In this question you should state clearly all the distributions that you use, together with the values of the appropriat…
  24. 24The speeds of an e-scooter (XX km/h) and a pedestrian (YY km/h) measured on a particular stretch of footpath are norma…
  25. 25In this question you should state the parameters of any distributions that you use. To regulate the use of its facil…
  26. 26Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  27. 27In an examination, the score, XX, for paper 1 of a student is found to follow a normal distribution with mean 62 and st…
  28. 28A sample of nn observations was taken from a population of mean μ\mu and variance 10. Find the least sample size requi…
  29. 29In this question you should state the parameters of any distributions you use. A snack company produces two types of…
  30. 30In this question you should state the parameters of any distributions that you use. To regulate the use of its facilitie…
  31. 31The table below shows the BMI-for-age for boys aged 18 years in Singapore. | Age (years) | Weight Indicator | Underweigh…
  32. 32Fruits 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…