4. Suppose the mathematics SAT scores are normally distributed with a mean of 50

Question

4. Suppose the mathematics SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. Assume your score is 550. Find your ranking (the percentage that below yours). 5. Suppose the mathematics SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. If you are among the top 15%, what is your score at least should be? 6. Suppose our first exam consists of 40 questions, each question has four possible answers (A,B,C,D), with only one is correct. Assume you pick your answers by random guessing, let X be your correct answers. Find the following probabilities a). P(X 12) b). PX 12)

Explanation / Answer

4)

hence 69.15% are below than you

5)

for top 15%; critical z =1.04

therefore corresponding score =mean+z*std deviation =500+1.04*100=604

6)

here fr porbability of correct answers p=1/4

hence mean number of correct answer =np=40*1/4 =10

and std deviation =sqrt(np(1-p))=2.739

hence from normal distribution and continuity correction:

a)P(X=12)=P(11.5<Z<12.5)=P(0.55<Z<0.91)=0.8186-0.7088=0.1098

b)P(X>=12) =1-P(X<11.5)=1-P(Z<0.55)=1-0.7088=0.2912

for normal distribution z score =(X-)/ here mean=       = 500 std deviation   == 100.000

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