Standard deviation formula when confidance level is given
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When the population standard deviation is known, the formula for a confidence interval (CI) for a population mean is

deviation, n is the sample size, and z* represents the appropriate z*-value from the standard normal distribution for your desired confidence level.
Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used.
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deviation, n is the sample size, and z* represents the appropriate z*-value from the standard normal distribution for your desired confidence level.
Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used.
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