Question

Find the z-score that has 82.89% of the distribution'a area to its right.

Answer 1

Given: The area to the right of z = 82.89% = 0.8289

To find the z score, the left side area is needed. The normal distribution is the symmetric distribution.

So the area under the normal curve is 100% that is 1.

So to get the left side area of the z, just subtract the right side area from 1.

Area to the left of z = 1 - 0.8289 = 0.1711

By using z score table, that is search 0.1711 or it's closest value in the middle body of a table and takes the corresponding row and column number. After that add both row and column number if the row number is negative then kept that sign outside and just add the numbers and then attach that negative sign to the final answer, which is the required z score.

By using z table the z-score for area 0.1711 to it's left is -0.95

Therefore, the z-score that has 82.89% of the distribution area to its right is -0.95