Statistic Question? Please help?

Question

7.. The mean score of a college entrance test is 500; the
standard deviation is 75. The scores are normally
distributed.

a. What percent of the students scored below 320?
b. Twenty percent of the students had a test score
above what score?
c. Ten percent of the students had a test score below
what score?

Answer 1

Break out your handy-dandy z-statistic table. This is the one that gives you the culumative probability of a normal distribution for a specific standard deviation.

1. Enough of the info onthe chart. For this problem, 320-500/75 is -2.4 standard deviations. The table will tell you the percent of students who score below this level.
2. This is the inverse problem, so you go to the distribution and find the z-score for cumulative probability = 0.8. If we call that R, then the score we want is SCORE-500/75=R.
3. This is similar to #2. Go to the distribution and find the z-score for cumulative probability = 0.1. If we call that R, the score we want will be
SCORE-500/75=R

Answer 2

a. the z-score for 320 can be found by using the equation: (320-500)/75... then you look on a z-score table and find the percent that is for that score.

b. & c. look at the z-score table and first find .080 in the big part of the table that tells percents and find the z-score that corresponds and solve backwards from the z equation: (x-mean)/sigma. for the 10% look for .010 then work backwards.