Math topic中文

Binomial mean variance

Use of mean and variance of binomial distribution (without proof).

Practice questions

  1. 1In a standardized assessment test conducted annually, it is found that, on average, 1 in 5 students who sit for the test…
  2. 2A fruit seller sources his oranges from a supplier with a large plantation where 1% of the oranges are rotten. The suppl…
  3. 3In each large batch of SIM cards, 15% of the cards are defective. From each batch, a random sample of 10 cards is drawn…
  4. 4Packets of a particular brand of potato chips are delivered to a supermarket in boxes of 60. On average, 1.8 packets in…
  5. 5The probability of obtaining a head when a particular coin is tossed is pp. A fair cubical die has the number '1' on on…
  6. 6在东京奥运会中，甲、乙、丙三名跳水运动员参加小组赛，已知甲晋级的概率为p(0<p<1)p(0< p< 1)，乙、丙晋级的概率均为q(0<q<1)q(0< q< 1)，且三人是否晋级相互对立. (1)若甲成功晋级的概率与乙、丙两人均没有晋级的概率相等，与乙、…
  7. 7A factory produces rectangular white marble floor tiles. The length of the floor tiles in centimetres can be regarded as…
  8. 8设随机变量 x～B(nx～B( n ， p)p)，若Ex=2.4Ex=2.4，Dx=1.44Dx=1.44则( ) A. n=4n=4， p=0.6p=0.6 B. n=6n=6， p=0.4p=0.4 C. n=8n=8， p=0.3p=0.3…
  9. 9On a Friday evening, the class chairperson emails his 20 classmates to propose an outing to watch a newly released actio…
  10. 10A small company makes wine glasses. Each day, n randomly chosen wine glasses are checked and the number of wine glasses…
  11. 11Green Earth Factory produces solar panels. On average, 2% of the solar panels produced are found to contain defects. The…
  12. 12Alice uses a computer program to simulate 80 tosses of a biased coin. Let YY be the random variable denoting the number…
  13. 13On a Friday evening, the class chairperson emails his 20 classmates to propose an outing to watch a newly released actio…
  14. 14A factory manufactures a large number of chips in a variety of colours and packs them into boxes. Each box contains 36 r…
  15. 15A biased die in the form of a tetrahedron has its four faces labelled 1 to 4, with one number printed on each face. The…
  16. 16A die is biased and the probability, pp, of throwing a six is known to be less than 16\frac{1}{6}. An experiment consis…
  17. 17In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
  18. 18On average, one in 40 scientific calculators manufactured by a company is faulty. An educational store manager decides t…
  19. 19Good Papa Caf'e sells only two types of muffins, chocolate and banana. The number of chocolate and the number of banana…
  20. 20A shop sells apples in bags of 12. The average number of unripe apples in a bag is 2.16. State two assumptions needed fo…
  21. 21One round of a game is played by randomly moving the counter from the starting point XX to one of the ending points AA…
  22. 22It is known that 8% of the population of a large city use a particular web browser called Voyager. A researcher wishes t…
  23. 23The National Aeronautics and Space Administration (NASA) compiles data on space shuttle launches and publishes them on i…
  24. 24Every 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…
  25. 25A supermarket sells boxes of a particular brand of biscuits in two flavours, chocolate and strawberry. The mean number o…
  26. 26On average, one in 40 scientific calculators manufactured by a company is faulty. An educational store manager decides t…
  27. 27Alex and Ben play with each other a set of ten games at table tennis and for each game, the probability that Ben loses i…