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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