Question

Hey, can someone please teach me this? I haven't been at school to learn it and I have a quiz later.

Example:
The scores on the SAT form a normal distribution with a mean of 500 and a standard deviation of 100.

What is the minimum score necessary to be in the top 15% of the SAT scores?

Find the range of values that define the middle 80% of the distribution of SAT scores.

Answer 1

604

Explanation:

"Top 15%" corresponds to the rightmost area under the standard normal curve to the right of the mean. That means 85% of the area under this curve will be to the left. Which z-score corresponds to the area 0.85 to the left?

Using a calculator (invNorm), find this z-score: invNorm(0.85) = 1.0346.

Which raw score corresponds to this z-score?

Recall the formula for the z-score:

x - mean

z = ------------------

std. dev.

Here we have:

x - 500

z = ------------------ - 1.0364, or x - 500 = 103.64. Then the minimum score

100 necessary to be in the top 15% of the scores is

found by adding 500 to both sides:

x = 603.64