Unit 2 Computations Review 1. A population distribution has a sum of squares of
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Unit 2 Computations Review 1. A population distribution has a sum of squares of 1617 with 33 scores and a mean of 21. What is the z score for an X-18? What percent of time would I score greater than 18? What percent of time would I score less than a 27? What is the percentile rank for a score of 32? What percent of scores fall below 16? What scores represent the middle 90%? What score would you have to get to be in the 78th percentile? What score is associated with a z--67? 6 2. Chris took 3 exams last week. On his Chemistry exam he had a z score of 0.54 On his History exam he scored a 35 when the mean was 27 and the standard deviation was 9. On his English exam Chris scored a 82. The mean of the English exanm vas rg and the standard deviation was 4. Rank Chris' performance from least to greatest Pat and Chris both took a spatial abilities test (mean-80. SD = 8). Pat scored a 76 and Chris scored a 94. What percent of individuals would score between Pat 3,Explanation / Answer
(1) here SS=1617 and n=33
SD=sqrt(SS/n)=sqrt(1617/33)=7
z=(X-mean)/SD
(first part)for X=18, z=(18-21)/7=-0.4286
P(X>18)=P(Z>-0.4286)=1-P(Z<-0.4286)=1-0.3341=0.6659
(second part)for X=27, z=(27-21)/7=0.8571
P(X<27)=P(Z<0.8571)=0.8043, required answer is 80.43%
(third part) X=32, z=(32-21)/7=1.57
P(X<32)=P(Z<1.57)=0.9418, so required answer is 94.17 percentile
(fouth part) X=16, z=(16-21)/27=-0.1852,
P(Z<-0.1852)=0.4265, anwer is 42.65%
(fifth part) middle 90% score means we want to find x1 and x2 such that
P(X<x1)=0.05 and P(X>x2)=0.05
now P(Z<z1)=0.05 that imply z1=-1.645 and x1=21-7*1.645=9.485
P(Z>z2)=0.05 that imply z2=1.645 and x2=21+7*1.645=32.515
(sixth part) P(Z<z)=0.78 and z=0.7722
and x=21+7*0.7722=26.41
(seventh part) z=-0.67, x=21-7*0.67=16.31
(2) for chemistry, z=0.54
for history, z=(35-27)/9=0.89
for english,z=(82-79)/4=0.75
so ranking of subjects are history, english, chemistry
(3) for x=76, z=(76-80)/8=-0.5
for x=94,z=(94-80)/8=1.75
P(76<X<94)=P(-0.5<Z<1.75)=P(Z<1.75)-P(Z<-0.5)=0.9599- 0.3085=0.6514
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