Exact and grouped call-duration statistics

Exact and grouped call-duration statistics

Secondary 2
13 marks
TGM Original Questions

Call durations (min) are 2, 4, 5, 5, 7, 8, 9, 10, 12, 13, 15, 15, 18, 20. For probability calculations, one of these calls is selected at random; let its duration be t minutes.

  1. Find the exact mean, median and mode(s).[4]
  2. Group them into \(0<t\le5,5<t\le10,10<t\le15,15<t\le20\), state the frequencies, draw a histogram, and estimate the mean using midpoints. Compare the estimate with the exact mean.[5]
  3. Find \(P(t>10)\) and \(P(5\le t\le15)\).[2]
  4. For 14 calls per day over 14 days, estimate how many exceed 15 min.[2]

Solution:

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Answer:(a) mean \(\frac{143}{14}\), median \(9.5\), modes \(5,15\) (b) histogram heights \(4,4,4,2\), estimate \(\frac{125}{14}\approx8.93\), about \(1.29\) below exact (c) \(\frac{3}{7},\frac{5}{7}\) (d) \(28\).

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