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Relative and Expected Frequencies MCQs — Mathematics (page 2)

42 multiple-choice questions on Relative and Expected Frequencies from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. From past records, the relative frequency of an event is 0.25. In 1200 future trials, it is expected to happen about:

  1. 600 times
  2. 25 times
  3. 900 times
  4. 300 times

Answer: D) 300 times

Explanation: 1200 0.25 = 300. SLO M-09-C-07 · Understanding

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27. From past records, the relative frequency of an event is 0.035. In 2000 future trials, it is expected to happen about:

  1. 4 times
  2. 70 times
  3. 140 times
  4. 1930 times

Answer: B) 70 times

Explanation: 2000 0.035 = 70. SLO M-09-C-07 · Understanding

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28. A card is drawn (and replaced) 520 times. The expected number of hearts is:

  1. 65
  2. 130
  3. 390
  4. 260

Answer: B) 130

Explanation: Expected frequency = n P = 520 14 = 130. SLO M-09-C-07 · Understanding

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29. A quality inspector expects 2% of bolts to be faulty. In a sample of 650 bolts she finds 13 faulty. This is:

  1. exactly the expected number
  2. more than expected
  3. fewer than expected
  4. impossible

Answer: A) exactly the expected number

Explanation: 650 0.02 = 13. SLO M-09-C-08 · Application

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30. A factory checks 400 items and finds 10 faulty. About how many faulty items should it expect in a batch of 12,000?

  1. 11700
  2. 600
  3. 100
  4. 300

Answer: D) 300

Explanation: Relative frequency = 10400; expected = 12000 10400 = 300. SLO M-09-C-08 · Application

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31. A farmer finds that 85% of his seeds germinate. If he plants 2400 seeds, about how many will not germinate?

  1. 2040
  2. 240
  3. 85
  4. 360

Answer: D) 360

Explanation: 15% of 2400 = 360. SLO M-09-C-08 · Application

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32. A bus is late on 9 of 60 days observed. Out of the next 200 days, on about how many days would you expect it to be late?

  1. 30
  2. 45
  3. 9
  4. 170

Answer: A) 30

Explanation: 960 = 0.15; 0.15 200 = 30. SLO M-09-C-08 · Application

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33. If an event has probability 0, its expected frequency in 1000 trials is:

  1. 1
  2. 500
  3. 1000
  4. 0

Answer: D) 0

Explanation: 1000 0 = 0. SLO M-09-C-07 · Understanding

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34. A factory checks 150 items and finds 3 faulty. About how many faulty items should it expect in a batch of 4,500?

  1. 90
  2. 4410
  3. 180
  4. 30

Answer: A) 90

Explanation: Relative frequency = 3150; expected = 4500 3150 = 90. SLO M-09-C-08 · Application

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35. From past records, the relative frequency of an event is 0.12. In 500 future trials, it is expected to happen about:

  1. 440 times
  2. 12 times
  3. 60 times
  4. 120 times

Answer: C) 60 times

Explanation: 500 0.12 = 60. SLO M-09-C-07 · Understanding

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36. From past records, the relative frequency of an event is 0.4. In 750 future trials, it is expected to happen about:

  1. 300 times
  2. 40 times
  3. 600 times
  4. 450 times

Answer: A) 300 times

Explanation: 750 0.4 = 300. SLO M-09-C-07 · Understanding

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37. If the expected number of heads in n tosses of a fair coin is 45, then n =

  1. 180
  2. 22.5
  3. 45
  4. 90

Answer: D) 90

Explanation: n 12 = 45 Rightarrow n = 90. SLO M-09-C-07 · Understanding

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38. A factory checks 200 items and finds 6 faulty. About how many faulty items should it expect in a batch of 5,000?

  1. 4850
  2. 300
  3. 150
  4. 60

Answer: C) 150

Explanation: Relative frequency = 6200; expected = 5000 6200 = 150. SLO M-09-C-08 · Application

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39. Expected frequency is calculated as:

  1. number of trials probability
  2. probability number of trials
  3. 1 - probability
  4. number of trials + probability

Answer: A) number of trials probability

Explanation: E = nP. SLO M-09-C-07 · Understanding

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40. Two dice are rolled 360 times. The expected number of double sixes is:

  1. 20
  2. 350
  3. 10
  4. 5

Answer: C) 10

Explanation: Expected frequency = n P = 360 136 = 10. SLO M-09-C-07 · Understanding

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41. A die is rolled 600 times and gives a six 180 times. What can you conclude?

  1. The expected number of sixes was 180
  2. The die is fair
  3. The die may be biased, because about 100 sixes were expected
  4. Sixes are less likely than other numbers

Answer: C) The die may be biased, because about 100 sixes were expected

Explanation: For a fair die, 600 16 = 100; 180 is far more than expected. SLO M-09-C-08 · Application

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42. A survey finds 36 of 150 households own a car. In an area of 2500 households, the estimated number of car owners is:

  1. 600
  2. 360
  3. 250
  4. 1900

Answer: A) 600

Explanation: 36150 = 0.24; 0.24 2500 = 600. SLO M-09-C-08 · Application

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