Given a distribution of scores with a mean of 40 and a standard deviation of 6, convert the following scores to the standard scores indicated:
a) X = 42 to a GRE score (a standard score with a mean of 500 and a standard deviation of 100)
b) X = 29 to an IQ score (a standard score with a mean of 100 and a standard deviation of 15)
Solution :
Given that ,
a) mean = = 40
standard deviation = = 6
x = 42
Using z-score formula,
z = x - /
z = 42 - 40 / 6
z = 0.33
= 500, = 100
Using z-score formula,
x = z * +
x = 0.33 * 100 + 500
x = 533
b) mean = = 40
standard deviation = = 6
x = 29
Using z-score formula,
z = x - /
z = 29 - 40 / 6
z = -1.83
= 100, = 15
Using z-score formula,
x = z * +
x = -1.83 * 15 + 100
x = 72.55
Given a distribution of scores with a mean of 40 and a standard deviation of 6,...
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