Question

A normal population with a population standard deviation of 25 is used to sample a population of 250 observations. 20 is the sample mean. With this determine the 95% confidence interval for the population mean.

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The confidence interval for the population mean when the population distribution is normal and the population standard deviation σ\sigma is known is given by

x±zσn,\overline{x}\pm z\cdot\dfrac{\sigma}{\sqrt{n}},

where x\overline{x} is the sample mean which is a point estimate of the population mean, the value of zz is found from the table of areas under the normal curve for the given confidence level, and nn is the number of observations in the sample.

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