scores on a SAT - statistics

Question

Scores on a SAT form a normal distribution of µ = 500 and σ = 100

 

1) What is the minimum score necessary to be in the top 20% of the SAT distribution?

 

2) find the range of value that defines the middle 60% of the distribution of scores

 

3)  Dan gets a score of 150 on the sat, what is his percentile rnak?

 

Please don't solve for me, rather help me solve them. I'm new to statistics and am unsure of what formula to plug these into or how to solve them.

 

 

Answer 1

 

Scores on a SAT form a normal distribution of µ = 500 and σ = 100

1) What is the minimum score necessary to be in the top 20% of the SAT distribution?

From the standard Normal Distribution Table you will find that area (probability) is 0.80000 when z  = 0.8416 (USING interpolation).  Use z = (X-μ) / σ to find X.

 

3) Dan gets a score of 150 on the sat, what is his percentile rank?

Pretty poor: z = (150-500) / 100 = -3.5 so area for him is 0.00034   Dan's at the bottom of the lowest 1%