Question

Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points. Suppose you take the SAT and several weeks later you receive a letter telling you that your results on the math portion of the test were in the 95th percentile.

Recalling that SAT scores are always expressed as multiples of 10, how many points did you get on the test? ...?

Answer 1

Explanation:

Given that Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points.

If X is the score in SAT, then X is N(500,100)

From std normal table we find 95th percentile as 1.645

i.e. your Z score = 1.645

Convert this to X score by
`X =1.645]\sigma + Mean\\= 1.645(100)+500\\=664.5`

Since expressed as multiples of 10, this equals 660

So points you got = 660

Answer 2

it's kinda hard because there is no z table available, but we can estimate around 1.64

p[95] = 664.4853

either 660 or 670

1.64 (100) = 164 + 500 = 664
i'd say that if you're within the p[95] the Score wil be 660

Hope this helps