Eleanor scores 660 on the mathematics part of the SAT. The distribution of SAT s

Question

Eleanor scores 660 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normal, with mean 575 and standard deviation 90. Gerald takes the America College Testing (ACT) mathematics test and scores 29. ACT scores are distributed with mean 20 and standard deviation 6. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score? Eleanor's score is higher Gerald's score is higher Eleanor's and Gerald's scores are the same Find the proportion of observations from a standard normal curve that satisfies z-score: 0.14

Explanation / Answer

19) as Z score =(X-mean)/std deviation

therefore Eleanor's z score =(660-575)/90=0.9444

Gerald z Score=(29-20)/6=1.5

therefore option B is correct

20)

P(0.14<Z<1.7)=0.9554-0.5557 =0.40

option C

21)

P(X>134)=P(Z>(134-98)/17)=P(Z>2.1176)=0.0171

therefore number of gifted student =np =2455*0.0171=42

option C

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