It depends on the shape of the distribution.
For standard normal distribution, a two tailed range would be from -1.15 sd to + 1.15 sd.
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To determine the number of observations needed to estimate the mean time for element 2 within 4 percent of its true value with 95.5 percent confidence, you would apply the formula for sample size: ( n = \left( \frac{Z \cdot \sigma}{E} \right)^2 ), where ( Z ) is the z-score corresponding to the desired confidence level (approximately 2 for 95.5%), ( \sigma ) is the estimated standard deviation, and ( E ) is the margin of error (in this case, 4 percent of the true mean). You would need an estimate of the standard deviation to calculate the exact sample size.
72
To do this, you first need to convert the percentage into a z-score. The bottom 10% yields a z-score of -1.2816. Multiplying this by 55 and adding to the mean gives 69.512. This means all score less that are 69 or less will be in the bottom 10%
I will restate your question as "Why are the mean and standard deviation of a sample so frequently calculated?". The standard deviation is a measure of the dispersion of the data. It certainly is not the only measure, as the range of a dataset is also a measure of dispersion and is more easily calculated. Similarly, some prefer a plot of the quartiles of the data, again to show data dispersal.t Standard deviation and the mean are needed when we want to infer certain information about the population such as confidence limits from a sample. These statistics are also used in establishing the size of the sample we need to take to improve our estimates of the population. Finally, these statistics enable us to test hypothesis with a certain degree of certainty based on our data. All this stems from the concept that there is a theoretical sampling distribution for the statistics we calculate, such as a proportion, mean or standard deviation. In general, the mean or proportion has either a normal or t distribution. Finally, the measures of dispersion will only be valid, be it range, quantiles or standard deviation, require observations which are independent of each other. This is the basis of random sampling.
That's on page 126 in your statistics textbook...... DO YOUR OWN HOMEWORK!!! K i obv needed help with how to do it, ass. I didn't want just the answer.