Discussion
The area under the standard normal curve between the lines at the points −1.96 and +1.96 is ................ .
Answer: C
The area between −1.96 and +1.96 is 95%.
From the standard normal table, the area from 0 to 1.96 is 0.4750. By symmetry the area from −1.96 to 0 is the same, so the total is 0.95, leaving 2.5 percent in each tail. This is why 1.96 is the critical value of z for a two-tailed test at the 5 percent level and for a 95 percent confidence interval.
5% is the area outside the two lines, not between them. About 90% lies between −1.645 and +1.645, and 50% lies on either side of the mean, so those options belong to other z values.
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