Suppose that scores on the quantitative SAT exam among students in Texas public

Question

Suppose that scores on the quantitative SAT exam among students in Texas public universities who are taking Calculus I have approximately a normal distribution with mean 580 and s.d. 80. [a] What proportion of such students scored above 720? [b] What are the quartiles of these scores? [c] Suppose there are 35 students in a particular section of Calculus I at UTD and the mean QSAT score for these students is 634 with a s.d. of 94. Treat this class as a random sample of students at UTD who take this course and construct a 95% confidence interval for the mean QSAT. How does the mean at UTD compare to the mean for all such students in Texas?

Explanation / Answer

a)P(X>720) =1-P(Z<(720-580)/80)=1-P(Z<1.75)=1-0.9599=0.0401

b)for 25 andf 75 % scores z=-/+ 0.6745

hence 1st quartile =25th percentiel =mean +z*std deviation =526.04

3rd quartile =633.96

c)for std error =std deviaiton/(n)1/2 =15.8889

for 95% CI and 34 degree of freedom t =2.0322

hence confidence interval =sample mean -/+ t*std error =601.71 ; 666.29

above interval gives 95% probabilty to contain mean for all students,

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