statistics
posted by Joanne .
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. Fortynine 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

Here's a few hints to get you started:
a. Find the zscores. Use the formula: z = (x  mean)/sd
z = (400  500)/100 = ?
z = (675  500)/100 = ?
Once you have the two zscores, look at the ztable to determine the probability between those two scores.
b. Check the ztable to determine the top 10%. Use that value for z. Use the zscore 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 zscore, check the ztable 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. 
Perfect advice. I appreciate the help!