Answer
A 99% confidence level means that the total area under the standard normal curve between two points (at the same distance) on different side of $\mu$ is 99%, or .99. To find the value of z for a 99% confidence level, we first find the areas to the left of these two points, -z and z. Then we find the z values for these two areas from the normal distribution table. The area between -z and z, 1-α =0.99. Hence, the total area in both tails is α = 1-.99=.01. Consequently, the area in each tail is 0.01/2 = 0.005. Then, the area to the left of -z is .0.005 and the area to the left of z is 0.005=.99 = .995
Now find the z values from the normal distribution table such that the areas to the left of -z and z are .005 and .995 respectively. These z values are -2.58 and 2.58, respectively.
Thus, for a confidence level of 99%, we will use z= 2.58 in the confidence interval formula.
Work Step by Step
--
