Answer :
Final answer:
The critical value z* for a confidence interval on the Normal distribution of 99.7% is approximately 2.967.
Explanation:
The 68-95-99.7 rule is a guideline for understanding the spread of data in a normal distribution. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and around 99.7% falls within three standard deviations.
To calculate the critical value z* for a confidence interval on the Normal distribution of 99.7%, we need to find the z-score that corresponds to the area of 0.997 under the standard normal curve.
The critical value z* can be found using a standard normal distribution table or a calculator. For a confidence interval of 99.7%, the area under the curve is 0.997. By looking up this area in the standard normal distribution table, we can find the corresponding z-score.
The critical value z* for a confidence interval on the Normal distribution of 99.7% is approximately 2.967.
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