Question

• Suppose I know that my son’s height is at the 65^th percentile for his age (that is, 65% of the kids his age is shorter than him). Then his z-score is _0.35845879.   Suppose I was at the 30^th percentile in height when I was 8 years old. That means that my z-score was ___.
• Hint: I find the z-score for the 84^th percentile by typing display invnormal(0.84)
• Hint: the proportion of grades between 2 SDs above the mean and 1 SD above the mean is (approximately) 13.5%, which I find by typing display normal (2) - normal (1) into Stata.
• ___% of all observations lie within 1 SD of the mean.
  ___% of all observations lie within 2 SDs of the mean.
  ___% of all observations lie within 3 SDs of the mean.
• In a quantile Normal plot, if the points of the variable lie along a ___ ___, more or less, then we have evidence that the variable is Normally distributed.
• In a quantile Normal plot, the more the points of the variable deviate from a straight line, the less the variable is __________ distributed.
• If a variable is right skewed (and takes only positive values), we can take a _____ to make it closer to Normally distributed.
• Compare GDP and log(GDP). log(GDP) is more _____ (right-skewed / symmetric) than GDP.

Answer 1

• Suppose I was at the 30th percentile in height when I was 8 years old. That means that my z-score was -0.5244005.
• Hint: the proportion of grades between 2 SDs above the mean and 1 SD above the mean is (approximately) 13.5%, which I find by typing display normal (2) - normal (1) into Stata.
• 68.26895% of all observations lie within 1 SD of the mean.
  95.44997 % of all observations lie within 2 SDs of the mean.
  99.73002% of all observations lie within 3 SDs of the mean.
• In a quantile Normal plot, if the points of the variable lie along a straight line, more or less, then we have evidence that the variable is Normally distributed.
• In a quantile Normal plot, the more the points of the variable deviate from a straight line, the less the variable is normally distributed.
• If a variable is right skewed (and takes only positive values), we can take a transformation to make it closer to Normally distributed.
• Compare GDP and log(GDP). log(GDP) is more symmetric  than GDP.