On the off chance that you know the standard deviation for a populace, at that point, you can compute a certainty interim (CI) for the mean, or normal, of that populace.

 At the point when a factual trademark that is being estimated, (for example, salary, level of intelligence, value, stature, amount, or weight) is numerical, a great many people need to evaluate the mean (normal) esteem for the populace. You gauge the populace mean,nfidence Interval for a Population Mean When You Know Its Standard Deviation

by using a sample mean,

plus or minus a margin of error. The result is called a confidence interval for the population mean,

plus or minus a margin of error. The result is called a confidence interval for the population mean,

When you  the population standard deviation, the formula for a confidence interval (CI) for a population mean is

image3.png

deviation, n is the sample size, and z* represents the appropriate z*-value from the standard normal distribution for your desired confidence level.

z*values for Various Confidence Levels
Confidence Levelz*-value
80%1.28
90%1.645 (by convention)
95%1.96
98%2.33
99%2.58

The above table shows estimations of z* for the given certainty levels. Note that these qualities are taken from the standard ordinary (Z-) dispersion. The territory between each z* esteem and the negative of that z* worth is the certainty rate (around). For instance, the territory among z*=1.28 and z=-1.28 is roughly 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used.

To calculate a CI for the population mean (average), under these conditions, do the following:

Determine the confidence level and find the appropriate z*-value.

Refer to the above table.

Find the sample mean

Multiply z* times

Multiply z* times

For instance, assume you work for the Division of Regular Assets and you need to evaluate, with 95% certainty, the mean (normal) length of all walleye fingerlings in a fish incubation facility lake. 

Since you need a 95% certainty interim, your z*-esteem is 1.96. 

Assume you take an arbitrary example of 100 fingerlings and establish that the normal length is 7.5 inches; expect the populace standard deviation is 2.3 inches. This implies 

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Increase 1.96 occasions 2.3 isolated by the square base of 100 (which is 10). The room for mistakes is, in this manner, 

image11.png 

Your 95% certainty interim for the mean length of walleye fingerlings in this fish incubation facility lake is 

image12.png 

(The lower end of the interim is 7.5 – 0.45 = 7.05 inches; the upper end is 7.5 + 0.45 = 7.95 inches.)

After you figure a certainty interim, ensure you generally translate it in words a non-analyst would get it. That is, talk about the outcomes as far as what the individual in the issue is attempting to discover — analysts consider this deciphering the outcomes “with regards to the issue.” In this example you can say: “With 95% certainty, the normal length of walleye fingerlings in this whole fish incubator lake is somewhere in the range of 7.05 and 7.95 inches, in light of my example information.” (Consistently make certain to incorporate proper units.)