Percentiles The test scores of 36 students from a calculus class are listed 4 4

Question

Percentiles The test scores of 36 students from a calculus class are listed 4 4 6 7 8 8 9 10 11 12 13 13 13 14 14 15 15 16 16 18 23 24 24 25 26 26 26 27 27 30 30 35 35 37 41 74 a) Find the score in the 20^th percentile. b) Find the percentile for the score of 9. Z-scores: The data from Problem #4 has a mean of 20.4 and a standard deviation of 13.5 a) Find the z-score of a person who scored a 54. b) Find the z-score of a person who scored a 95. c) Recall that the range of usual values are two standard deviations from the mean. Find the range of usual values.

Explanation / Answer

a) as 20th percentile score =(n+1)*0.2 th value =(36+1)*0.2 th value =7.4 th value =9+0.4*(10-9)=9.4

b)as 9 is 7th score hence its percentlie =7/37 =18.9 percentile

5)a) zscore=(X-mean)/std deviation=(54-20.4)/13.5=2.4889

b)=(95-20.4)/13.5=5.5259

c) two std deviation away values =20.4-2*13.5 ; 20.4+2*13.5 =-6.6 ; 47.4

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