Statistics for Business

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Does asymptotic mean that the normal curve gets closer and closer to the X-axis but never actually touches it?

Yes, asymptotic means that the curve of a line will approach 0 (the x-axis), but it will not touch 0 and instead will extend to infinity. In this class, this applies to the normal continuous distribution and is one of the 4 key characteristics of a normal continuous distribution that our text book discusses. This means that the curve of the line will extend infinitely in both the negative and positive direction in exact mirror image patterns on either side of the mean.

For a normal probability distribution, is about 95 percent of the area under normal curve within plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area under the normal curve is within three standard deviations of the mean?

Yes. According to the Empirical Rule:
-68% of the area under the curve is within +/- 1 standard deviation of the mean -95% of the area under the curve is within +/- 2 standard deviations of the mean -Virtually all, 99.7% of the area under the curve is within +/- 3 standard deviations of the mean

Is a z-score the distance between a selected value (X) and the population mean (u) divided by the population standard deviation(s)? Yes. We use z-scores to change normal probability distributions into standard normal probability distributions, which are unique because they have a mean of 0 and standard deviation of 1. To convert to a standard normal probability distribution we must find the z-scores for each observation. These are found by subtracting the mean value from the selected value and dividing by the standard deviation.

The Normal Probability Distribution
Find an example of application of probability theory in your workplace or business. Show that the reasons that your workplace uses probability analysis, such as probability of risk calculations or percent defects or percent for pass or fail of a...
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