Normal Distributions: Finding Values Data from a state indicate that scores on t

Question

Normal Distributions: Finding Values Data from a state indicate that scores on the SAT test are normally distributed with a mean of 1003 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 22.8 and a standard deviation of 4.7. It is assumed that the two tests measure the same aptitude, but use different scales If a student gets an SAT score that is the 26 percentile, find the actual SAT score. Round answer to a whole number SAT score = What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score- If a student gets an SAT score of 1340, find the equivalent ACT score. Round answer to 1 decimal place. ACT score

Explanation / Answer

SAT test

mean 1003

sd 198

ACT test

mean 22.8

sd 4.7

a)

P(Z<z)= 0.26

z= =NORMSINV(0.26)

z= -0.643345405

I know that z=(X-mean)/sd

hence, (X-mean)/sd = -0.643345405

X = =-0.64335*198+1003

X = 876

b)

P(Z<z)= 0.26

z= =NORMSINV(0.26)

z= -0.643345405

I know that z=(X-mean)/sd

hence, (X-mean)/sd = -0.643345405

X = =-0.64335*4.7+22.8

X = 20

c)

z score compares 2 variables measured on different units.

for SAT, z= (X-mean)/sd

z= =(1340-1003)/198

z= 1.702020202

for ACT, x = z*sd + mean

X= =1.70202*4.7+22.8

X= 30.8

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