Answer a. Yes, the area beyond a Z = .23 to the tail is .409 per the
Standard Normal Curve table. Note that you have to consider the absolute value of the tabled areas because the tabled areas apply to both sides of the normal distribution of Z scores (i.e., the distribution is perfectly symmetrical).
b. No, this is the area between Z and the mean for Z = .23. We care about the area in the tail to find out the proportion you did better than.
c. No, this is the proportion higher than Z = .23, and is irrelevant here.
d. No, this is irrelevant.
e. No, (a) is correct.
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Answer a. No, the Z score is not just the percentage.
b. Yes, if you did better than 79.1% of the scores, then you did better
than .791 proportion of the area under a normal curve. You know that if you are above the mean then you must have done better than .500. So, now all you need to find out is the area between the mean and where your Z score is, or .791 - .500 = .291. The area between the mean and your Z is therefore .291. Now you can use the Standard Normal Curve table to find out what Z score would you have if you have a proportion of .291 between you and the mean. Just scan the table column for “Area between Mean and Z” until you find .291. The Z score associated with this is Z = .81. It probably would help tremendously if you also sketched out the distribution and marked the areas you are considering – much like the distributions in this presentation.
c. No, irrelevant.
d. No, irrelevant.
e. No, (b) is correct.

Unit 5: Distributional ShapeLesson 5:Probability and the Normal Curve :

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