1. Test scores for women on the verbal portion of the SAT-1 test are normally di
ID: 2933802 • Letter: 1
Question
1. Test scores for women on the verbal portion of the SAT-1 test are normally distributed with a mean of 502 and a standard deviation of 109 (based on data from the College Board). Twenty-five randomly selected women are given the Columbia Review course before taking the SAT test. Assume that the course has no effect. a. If one women is randomly selected, find the probability that her score is at least 535. b. If 25 women are randomly selected, find the probability that their mean score is at least 535. c. In finding the probability for part (b), why can the central limit theorem be used even though the sample size does not exceed 30? If the random sample of 25 women does result in a mean score of 535, is there strong evidence to support the claim that the Columbia Review course is actually effective? Why or why not?
Explanation / Answer
a) probability that her score is at least 535=P(X>535)=1-P(X<535)=1-P(Z<(535-502)/109)
=1-P(Z<0.3028)=1-0.6190 =0.3810
b)
for std error of mean =std deviation/(n)1/2 =109/(25)1/2 =21.8
hence probability that their mean score is at least 535 =P(X>535)=1-P(X<535)=1-P(Z<(535-502)/21.8)
=1-P(Z<1.5138)=1-0.9350 =0.0650
c)
as population is normally distributed threfore we can apply central limit theorem even though the sample size does not exceed 30.
as for random sample of 25 women does result in a mean score of 535 has probability greater then 0.05 level threfore it can not be considered as an unusal event and therefore there is not strong evidence to support the claim that the Columbia Review course is actually effective
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