Mean = 70.07, and standard deviation = 10.27, find the percentage of students wh
ID: 3056908 • Letter: M
Question
Mean = 70.07, and standard deviation = 10.27, find the percentage of students who did (a) very well, scoring above 85, and (b) those students who did poorly, scoring below 50.
1. Find the raw score that bounds the top 10 percent of the distribution.
2. Find the raw score that bounds the lowest 5 percent of the distribution.
3. Suppose your raw score was 85. You want to calculate the percentile (i.e., the percentage of students in class that score below you).
4. Now, suppose your raw score was 65. Calculate the percentile.
5. Say you need to score in the 95th% to be accepted to a particular
grad school program. What’s the cutoff for the 95th%?
6. What score is associated with the 40th%?
Explanation / Answer
1) for top 10% ; zscore =1.2816
value =mean +z*std deviation =83.23
2) for lowest 5% ; zscore =-1.6449
value =mean +z*std deviation =53.18
3)
for score 85 ; zscore =(X-mean)/std deviation =1.4537
corresponding percentile =92.70
4)
for score 65 ; zscore =(X-mean)/std deviation =-0.4937
corresponding percentile =31.08
5)
for 95 th% ; zscore =1.6449
value =mean +z*std deviation =86.96
6)
for 40th percentile ; zscore =-0.2533
value =mean +z*std deviation =67.47