# SAT I scores aroung the nation tend to have a mean scale around 500 standard deviation 100 & approximatley normally distributed. continueda person who scores 600 on the SAT I has...

SAT I scores aroung the nation tend to have a mean scale around 500 standard deviation 100 & approximatley normally distributed.

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a person who scores 600 on the SAT I has approximatelt what percentile rank within the population ? show all work as to how it was obtained

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### 1 Answer

We can convert the score of 600 to a standard score: `z=(X-bar(x))/s` where x=600,`bar(x)=500` , and s=100.

Then `z=(600-500)/100=1` . A student with a SAT score of 600 scores 1 standard deviation above the mean.

We can use a standard normal chart to find the percentage of scores that will be less than 600. The probability that a random score is less than 600 `P(x<600)` is the percentage of the population that scores below 600.

But `P(x<600)=P(z<1)` . And the probability that z<1 can be found by finding the area to the left of z=1 under the standard normal curve; this is given by the standard normal table.

`P(z<1)~~.8413` (from the table or algebra system)

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**A student who scores a 600 on the SAT is in the 84th percentile**

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