A grading scale is set up for 1000 students' test scores. It is assumed that the scores are normally distributed with a mean score of 75 and a standard deviation of 15.
1. How many students will have scores between 45 and 75?
2. Assuming a 90% is an A, about how many students are expected to pass?
3. Would it be likely that a typical high school teacher to have normally distributed test scores amongst all of his/her classes? Why or why not?
I'm having a bit of a problem with this problem. If you know what you're doing with standard deviation please help me out. Thanks alot!
2006-12-16 05:08:56 · 3 answers · asked by crazy8s622 2 in Science & Mathematics ➔ Mathematics
1. By empirical rules, 95% of all the variation lies between -2 and +2 standard deviations of the mean. So if you're looking from 45 to 75, you are looking from -2 standard deviations to the mean which is half of the range described above = 95%/2 = 47.5%
2. also by the empirical rule, 68% of the data lies within one standard deviation of the mean. So if 90 is an A, that means 60 is a D- and the lowest passing score. -1 to 1 = 68%, -1 to 0 = 34%. then from 0 to infinity = 50%. 50% + 34% = 84%
3. Yes it would be likely. The large number of students in all the classes, according to the central limit theorem, would tend to a normal distribution
2006-12-16 05:18:06 · answer #1 · answered by Modus Operandi 6 · 0⤊ 0⤋
At least 75% of the values in any population are at most two standard deviations away from the mean.
75% of 1000 = 750 students within 2 SD of the mean.
Mean test score = 75
1 SD to the right gives you test scores between 75 and 90
1 SD to the left gives you test scores between 75 and 60
2 SD to the right gives you test scores between 75 and 100
2 SD to the left gives you test scres beween 75 and 45
You can easily do the remaider of the problem from here because I don't know what a passing grade is...60? 70?
2006-12-16 05:36:56 · answer #2 · answered by robert k 2 · 0⤊ 1⤋
173, Mensa the front exam. yet massive deal. i'd extremely have a a sunny disposition, a gorgeous face and massive **** any day. earn extra money that way. As is, i'm a detrimental, semi-depressing genius. Whoop de doo.
2016-11-30 20:40:28 · answer #3 · answered by ? 4 · 0⤊ 0⤋