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Step #5: Find the Z value for the selected confidence interval. Confidence IntervalZ85%1.44090%1.64595%1.96099%2.5763 more rows ? 11-May-2018

To capture the central 90%, we must go out 1.645 ?standard deviations? on either side of the calculated sample mean. The value 1.645 is the z-score from a standard normal probability distribution that puts an area of 0.90 in the center, an area of 0.05 in the far left tail, and an area of 0.05 in the far right tail.

A 95% confidence interval for the standard normal distribution, then, is the interval (-1.96, 1.96), since 95% of the area under the curve falls within this interval.

Your estimate for the lower bound of the 99% confidence interval should be less than 0.065, and your estimate for the upper bound should be greater than 0.157. The value of the factor z from the standard Normal distribution for a 99% confidence interval is 2.576.

?p±z??p(1??p)n, where the value of z is appropriate for the confidence level. For a 95% confidence interval, we use z=1.96, while for a 90% confidence interval, for example, we use z=1.64.

A continuous random variable Z is said to be a standard normal (standard Gaussian) random variable, shown as Z?N(0,1), if its PDF is given by fZ(z)=1?2?exp{?z22},for all z?R. The 1?2? is there to make sure that the area under the PDF is equal to one.

The standard normal distribution table is a compilation of areas from the standard normal distribution, more commonly known as a bell curve, which provides the area of the region located under the bell curve and to the left of a given z-score to represent probabilities of occurrence in a given population.