mba 522 Normal Examples- starter set - Dr J 1 Normal...

Dr. J.
Normal Distribution: Two Examples
I cannot emphasize the importance of understanding the normal curve, and the ability to
apply it and z-values. You will use it throughout your curriculum, so you must get a good
handle on it.
To do z-applications, it is best to draw a normal curve and use it as a key to conduct your
analysis. For the examples which follow, I have drawn curves so you can visually see
what we are trying to answer. The graphs for each problem appear at the bottom of the
problem.
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Example number one
Assume a sample of 10 NBA game scores resulted in an average score of 96.8 and a
standard deviation of 8.22. Also assume that game scores are normally distributed.
The question is: what is the percentage of all NBA games in which the winning team will
score 105 or more points.
The answer is 16%. This is how you can arrive at that answer. My normal distribution
sketch for this problem can be seen if you scroll down.
1. Draw a normal (bell-shaped) curve.
2. All the way to the left of the curve on the horizontal axis write "game scores" to
indicate that this distribution and its values represent game scores. Also mark the center
of the horizontal axis. Below it write 96.8 (this indicates that the average game score is
96.8).
3. Somewhere to the side of curve write sigma=8.22 (as a reminder to yourself of the
standard deviation for this distribution).
4. The number that you are interested in is a score of 105. The question asks what is the
probability that a score higher than 105 will be made! So, mark 105 on the horizontal
axis. Since 105 is a bigger value than 96.8, you should mark a point somewhere to the
right of the mean. Below it write the number 105.
5. Draw a vertical line from that point up to the curve.
6. Shade the appropriate area. In this case, you are interested in the percentage
(probability) that a team scores higher than 105. Higher than 105 would be the area to the
right of 105. So, shade that area under the curve from 105 to the right tail of the curve.