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WAEC 2023 · Paper 2 · Q13

  1. (a)

    The mean of four consecutive odd numbers is 6. Find, correct to one decimal place, their variance.

  2. (b)

    The table shows the distribution of marks obtained by a group of candidates in an examination.

    Marks 0–19 20–39 40–59 60–79 80–99
    Number of candidates 8 14 18 6 4

    If three candidates are selected at random from the group, find, correct to three decimal places, the probability that two of them are from the modal class.

Worked solution (try it first)

(a)

  1. Four consecutive odd numbers with mean 6 are 3,5,7,93, 5, 7, 9.
  2. Their deviations from 6 are −3,−1,1,3-3, -1, 1, 3, so the variance is 9+1+1+94=5.0\dfrac{9 + 1 + 1 + 9}{4} = 5.0.

(b)

  1. The modal class is 40–59, with 18 of the 50 candidates.
  2. There are (503)=19 600\binom{50}{3} = 19\,600 ways to choose 3.
  3. Two from the modal class and one from the other 32: (182)×32=153×32\binom{18}{2} \times 32 = 153 \times 32
    =4896= 4896.
  4. So P=489619600≈0.250P = \dfrac{4896}{19600} \approx 0.250.

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