Normal Distribution Example

Question

The SAT scores follow N (1100,200)

(a) What is the 95th percentile for SAT scores ?

(b) What is the 97.5th percentile for SAT scores ?

Answer 1

Hi Carlie,

In order to solve this problem, we need to realize a few things:

1. N(1100, 200) translates to µ = 1100 and σ = 200
2. the 95th percentile translates to a probability (i.e. area under the curve) of 0.95
3. the 97.5th percentile translates to a probability (i.e. area under the curve) of 0.975

a) an area under the curve of 0.95 translates to a Z-score of 1.645

1.645 = ((x-bar) - 1100) / (200) --> x-bar = 1429

The 95th percentile for SAT scores would be 1429.

b) an area under the curve of 0.975 translates to a Z-score of 1.96

1.96 = ((x-bar) - 1100) / (200) --> x-bar = 1492

The 97.5th percentile for SAT scores would be 1492.