Statistics - Probability Problem w/ Random Sampling?

Question

Can someone please help me with this problem: Scores on the SAT college entrance exam in a recent year were roughly Normal with 1026 and a standard deviation 209. You choose a random sample of 100 students and average their SAT scores. What is the probability that a randomly selected score is between 1005 and 1100?

Answer 1

You need to convert your data into a z-score, and then use the table for the probability.

Z = (Sample mean - Population Mean) / SD

Z = (1005-1026) / 209 = -.1004 and

Z = (1100-1026) / 209 = .3540

The z sign (positive or negative) will tell you how far away from the mean you will be: So, the first one is to the left, and the second to the right.



Using a z-table, we find the probabilities to be:

-.1004 = .540, which means 54% of scores are to the right of 1005.

.354 = . .638, which means 63% of scores are to the left of 1100.

This means that 63 - 54 % = 9% of scores fall within this range.

Regards,

Mysstere