the distribution of SAT scores is approximately normal with a mean of ?=500 The

Question

the distribution of SAT scores is approximately normal with a mean of ?=500 The distribution of SAT scores is approximately normal with a mean of ? = 500 and ?-100. For the population of students who have taken the SAT, 4 a. What proportion have SAT scores greater than 700? b. What proportion gave SAT scores greater than 5507 wat is the minimum SAT score needed to be in the highest 10% of the population? c if the state college only accepts students from the top 60% of the SAT distribution, what is the minimum SAT score needed to be accepted? d,

Explanation / Answer

Ans:

Given that

mean=500

standard deviation=100

a)

z=(700-500)/100=2

P(z>2)=0.0228

b)

z=(550-500)/100=0.5

P(z>0.5)=0.3085

c)

P(Z>z)=0.1

P(Z<=z)=1-0.1=0.9

z=normsinv(0.9)=1.282

minimum score required to be in top 10%=500+1.282*100=628.2

d)

P(Z>z)=0.6

P(Z<=z)=1-0.6=0.4

z=normsinv(0.4)=-0.2533

minimum score required to be in top 60%=500-0.2533*100=474.67

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