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Normal Distribution · CAPE Applied Mathematics Unit 1

39 past-paper questions on Normal Distribution, part of Module 2: Managing Uncertainty, from every CAPE Applied Mathematics Unit 1 paper on Quelpr.

Practise Normal Distribution
  1. 4(a)5 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Show that the probability of a randomly selected bottle containing more than 99.8 ml of pepper sauce is approximately 0.516.
  2. 4(b)6 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Eighty-one per cent of the bottles contain less than k ml of pepper sauce. Calculate the value of k.
  3. 4(d)6 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2The mass of a loaf of bread follows a normal distribution with mean 480 g and standard deviation 20 g. Calculate the probability that a randomly chosen loaf has mass between 465 g and 500 g.
  4. 4(c)3 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2The random variable X has a normal distribution with mean 12 and variance 4. Find the constant c such that P(X < c) = 0.9332.
  5. 4(d)(i)5 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2What is the probability that a rod selected at random will measure more than 65 centimetres?
  6. 4(d)(ii)5 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Rods that are less than 54 centimetres are cut and sold as a smaller length. What percentage of rods will have to be cut?
  7. 5(d)(ii)5 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Calculate P(X̄ > 4.5).
  8. 4(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2State TWO conditions that should exist for the normal distribution to be used as an approximation for the binomial distribution.
  9. 4(c)(ii)7 marks· CAPE Applied Mathematics Unit 1 · 2010 · Paper 2The probability that a pen is faulty is 0.06. In a box of 100 pens, what is the probability that at MOST 5 pens will be faulty?
  10. 3(c)7 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2If 95 matches are selected at random, use a suitable approximation to calculate the probability that between 14 and 21 (inclusive) of the matches are won.
  11. 4(b)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Calculate the probability that a cabbage chosen at random will have a weight greater than 650 grams.
  12. 4(b)(ii)5 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Twenty per cent of cabbages were classified as large. Calculate the weight that these cabbages must exceed to be classified as large.
  13. 4(b)(iii)5 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Calculate the probability that a cabbage weighs between 610 grams and 650 grams.
  14. 4(b)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2A supermarket buys cabbages between 610 and 650 grams. If a farmer has 65 cabbages for sale, determine the number expected to be sold to the supermarket.
  15. 4(c)(iii)6 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Using an approximate distribution, calculate an estimate for the probability that a shipment of 500 tyres will have more than 90 defective tyres.
  16. Q161 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1Which of the following statements describe the main features of the normal distribution? I. It is bell-shaped. II. It is symmetrical about the mean. III. The total area under the curve is 1. IV. It extends from 0 to…
  17. Q241 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The heights of rose plants follow a normal distribution with mean 215\text{ cm} and standard deviation 20.2\text{ cm}. The probability, to 3 significant figures, that the height of a randomly chosen rose plant is…
  18. Q301 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1If X \sim \text{N}(20, 16), and P(X > w) = 0.119, then the value of w is
  19. 4(c)5 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2The lifespan of an insect species follows a normal distribution with mean 72 days and standard deviation 8 days. Calculate the probability that an insect lives for more than 84 days.
  20. 4(d)(iii)6 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Use an approximate distribution to calculate the probability that less than 175 seeds from the package will germinate.
  21. Q191 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1If Z \sim N(0, 1), then P(-1 < Z < 2) is given by
  22. Q291 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1If X \sim N(35, 56), then P(X < 33) is given by
  23. 4(c)7 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Determine the percentage of students who will get a Grade A.
  24. Q161 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1Which of the following statements describe the main features of the normal distribution? I. It is bell-shaped. II. It is symmetrical about the mean. III. The total area under the curve is 1. IV. It extends from 0 to…
  25. Q201 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1When the normal distribution is to be used as an approximation to the binomial distribution, the P(40 < X \le 45) becomes
  26. Q251 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1If X \sim N(24, 36), then P(X > 25) is
  27. Q211 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1If Z \sim N(0, 1), then P(-3 < Z < -1) is
  28. Q241 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1If Z \sim N(0, 1), the figure illustrating P(Z > a) = 0.35 is
  29. Q301 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1If X \sim N(20, 16), and P(X > w) = 0.119, then the value of w is
  30. 4(b)5 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2The mass, X, of packages of a certain type of breakfast cereal follows a normal distribution with a mean of 60 g and a standard deviation of 5 g. Calculate the probability that a package chosen at random has a mass of…
  31. 4(c)(iv)7 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Five hundred seedlings are sent to KG's Gardens. Determine the mean and the variance of the number of seedlings that will NOT survive transplantation, and find the probability that less than 55 seedlings will NOT…
  32. Q201 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1When the normal distribution is to be used as an approximation to the binomial distribution, the P(40 < X \le 45) becomes
  33. 4(a)(vi)7 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2For a sample of 100 customers, use a suitable approximation to determine the probability that no more than 35 customers make their monthly payments on time, stating all your assumptions.
  34. 4(b)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the probability that a javelin selected at random will measure more than 255 cm.
  35. 4(b)(ii)4 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Javelins less than 220 cm are cut and sold as fence posts. Calculate the percentage of javelins that will have to be cut and sold as fence posts.
  36. 4(a)(iii)6 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Use a suitable approximation to find the probability of FAILING to get the intended number on at least 10 but NOT more than 20 of the calls.
  37. 4(b)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2If it was found that 0.19% of the computers on a particular occasion had a repair time that was less than 24 hours, show that sigma = 5.5 (to one decimal place).
  38. 4(b)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Find the probability that the repair time is MORE than 35 hours.
  39. 4(b)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2CompuFix wishes to state in its advertisements that at LEAST 98% of all computers will be repaired in less than a certain number of hours. Determine the SMALLEST integer that could truthfully be used in the…

Related topics in Module 2: Managing Uncertainty