Posted by **Joanne** on Monday, August 4, 2008 at 9:17pm.

SAT scores are normally distributed. The SAT in English has a mean score of 500 and a standard deviation of 100.

a. Find the probability that a randomly selected student's score on the English part of the SAT is between 400 and 675.

b. What is the minimum SAT score that a student can receive in order to score in the top 10%?

c. Forty-nine students are sampled. Find the probability that their mean score for the SAT is less than 470.

I have the following answers, but do not know how they were derived:

a. 0.8013

b. 628

c. 0.0179

- statistics -
**MathGuru**, Monday, August 4, 2008 at 9:47pm
Here's a few hints to get you started:

a. Find the z-scores. Use the formula: z = (x - mean)/sd

z = (400 - 500)/100 = ?

z = (675 - 500)/100 = ?

Once you have the two z-scores, look at the z-table to determine the probability between those two scores.

b. Check the z-table to determine the top 10%. Use that value for z. Use the z-score formula. You will have z, the mean, and the standard deviation. Solve the formula for x.

c. Formula: z = (x - mean)/(sd/√n)

With your data:

z = (470 - 500)/(100/√49) = ?

Once you have the z-score, check the z-table for the probability. Remember that this problem is looking for "less than" 470, so keep that in mind when looking at the table.

I hope this will help.

- Thank you -
**Joanne**, Monday, August 4, 2008 at 11:14pm
Perfect advice. I appreciate the help!

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