The population distribution of individual SAT scores raw sco

The population distribution of individual SAT scores (raw scores) has population mean of 500 and a population standard deviation of 100. You select a sample of size 100 (N = 100).

a) Out of all of the possible sample means in this sampling distribution, what value will have 70% of the sample means falling at or below it?

b) What value will have 70% of the sample means falling at or above it?

Solution

Mean = 500

Stdev = 100

n=100

a) P(X<=k) = .7, k=?

From Z tables, Z=.525

So, (k - 500 )/ (100/sqrt(100)) = .525

k = 505.25

So, a SAT score of 505.25 will have 70% of sample means falling below it.

b) Remember its a symterical distribution. Instead of 70% and below, we are calc. 70% above a value.

So, (500 - k )/ (100/sqrt(100)) = .525

k = 500-5.25

=494.5

70% of the sample means falling at or above the value of SAT score = 494.5