Answer
a) Mean:75, standard deviation:10.
b)No.
c)45.2 and 52.8.
d)the method in c)
Work Step by Step
a)If we add 35 to each grade, the mean also increases by 35, it becomes 40+35=75, but the standard deviation remains 10.
b)No, because the standard deviation stays the same, hence the scores are not curved.
c) By using the table, the z-score corresponding to 0.7 and 1-0.1=0.9: z=0.52 and z= 1.28. Hence the corresponding values:$mean+z⋅standard \ deviation=40+0.52⋅10=45.2.$
$mean+z⋅standard \ deviation=40+1.28⋅10=52.8.$
d) Using the method in c) takes the variation into consideration, whilst the other method doesn't.
