2. Over a period of many months, a particular 5 year old boy\'s play ac tivity w

Question

2. Over a period of many months, a particular 5 year old boy's play ac tivity 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 Length of time spent in play-episode (seconds) 0 less than 5 5 less than 10 10 - less than 15 15 - less than 20 20 - less than 40 40 less than 60 60 less than 90 90 less than 120 120 - less than 180 Frequency 54 28 21 31 15 16 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. 3·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.

Explanation / Answer

a) fraction of student score above 140 points =P(X>140)=1-P(X<140)=1-P(Z<(140-122)/18=1-P(Z<1)=1-0.8413

=0.1587

b)

for bottom 15 percentile ; critical z =-1.0364

hence corresponding cutoff score =mean +Z*std devaition =122-1.0364*18 =103.34

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