SOLUTION: Suppose that a test to measure a student's motivation to do well in school was administered to grade 11 high school students. The scores are normally distributed with a mean of 200

Question 1063652: Suppose that a test to measure a student's motivation to do well in school was administered to grade 11 high school students. The scores are normally distributed with a mean of 200 and a standard deviation of 15.
a. What is the range of scores of the students who achieved the middle 60% of all scores?
b. If the score of one student is lower than that of 35% of the group who took the test, what was the student's score?
c. What is the probability that a randomly selected student scored at least 210 in the test?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
From the z-table, the middle 60% (from 20 percentile to 80 percentile) has a z value between +/- 0.842
multiply that by the sd, and the score is 200+/-12.63, or (187.4, 212.6)
z=-.385 for the 35th percentile, again from the table.
-.385=(x-200)/15
-5.775=x-200
x=194.2
To score at least 210 means to be 2/3 of 1 sd above the mean. That is a probability of 0.2525.
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