Question

1-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... Frequency Relative Frequency Density Length of time spent in play-episode (seconds) 0-less than 5 54 5-less than 10 44 10-less than 15 28 15-less than 20 20-less than 40 40-less than 60 21 31 15 60-less than 90 16 90-less than 120 120-less than 180 5 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 2. To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 15% of the students in the district, based on the scores on a reading achievement exam given in the child's dominant language. The reading score for the pooled students in the district is approximately normally distributed with a mean of 122 points, and standard deviation of 18 points a. What fraction of students score above 140 points? b. Find the cutoff score that will make a student eligible for the program?

Answer 1

Answer:

1)

Class interval Frequency X 0-5 2.5 54 5 - 10 7.5 44 10 15 12.5 15 20 17.5 21 20 40 30 31 40 60 50 15 75 60-90 16 90-120 105 5 120 180 150 Total frequency= 222 Ln CO 28

(a) Density histogram is obtained by dividing each frequency by total frequency, i.e., 222 as below: density X 2.5 0.2432 7.5 0.1982 0.1261 12.5 17.5 0.0946 0.1396 30 50 0.0676 0.0721 75 105 0.0225 0.0360 150 (b) Proportion of play-episodes that lasted at most 75 seconds P(X < 75) 0.2432 0.1982 0.0946 0.1396 0.0676 +0.0721 0.1261 0.9414