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Over a period of many months, a particular 5 year old boy\'s play activity was o

ID: 3180129 • Letter: O

Question

Over a period of many months, a particular 5 year old boy's play activity was observed. The length of time spent in each episode of play with toys was recorded. The paper "A Temporal Analysis of Free Toy Play and Distractibility in Young Children" (Journal of Experimental Child Psychology, 1991, pages 41-69) reported the accompanying data on the play-episode lengths. a. Display this information in a density histogram. b. Use the density histogram to estimate the proportion of play-episodes that lasted at most 75 seconds.

Explanation / Answer

Class interval       x         Frequency         

   0 - 5               2.5             54

   5 - 10             7.5              44

   10 - 15           12.5            28

   15 - 20            17.5            21

20 - 40               30             31

40 - 60               50             15

60 - 90               75             16

90 - 120             105               5

120 - 180              150            8

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Total frequency =                 222

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(a) Density histogram is obtained by dividing each frequency by total frequency, i.e., 222 as below:

   x                  density

    2.5                 0.2432

    7.5                0.1982

    12.5                0.1261

17.5                    0.0946

30                       0.1396

50                        0.0676

75                       0.0721

105                      0.0225

150                       0.0360

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(b) Proportion of play-episodes that lasted at most 75 seconds = P(X < 75) = 0.2432 + 0.1982 + 0.1261 + 0.0946 + 0.1396 + 0.0676 + 0.0721 = 0.9414

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