standard deviation

Question

scores on a test are being normally distrubuted. mean 73.0 standard deviation 5.0. 100 students were tested. how many students scored between 68 and 78?  how many students scored below 63?

 

 

Answer 1

68 = mean -1 standard deviation (73-5)

78 = mean + 1 standard deviation (73+5)

total # of students tested = 100

 

in a normal distribution, 68% of values are within 1 standard deviation of the mean.

So, # students who scored between 68 and 78 = 68% of 100 = 68

 

 

63 = mean - 2 standard deviation (73-2*5)

50% students scored above mean (=median for normal distribution)  ----(1)

95% scored within 2 standard deviations of mean (between 63 and 83)

  - 95/2 = 47.5% scored between 63 and 73 -----------------------------(2)

 

Combining (1) and (2), 50+47.5=97.5% scored above 63

Therefore, 100-97.5 = 2.5 score less than 63