Statistics problems, please urgent help needed

Question

1.For a standard normal distribution, find the z-value that corresponds to the lower 18.22 % of the data. Round your answer to two decimal places.

2.For a standard normal distribution, find the z-value that corresponds to the upper 6.85 % of the data.

Round your answer to two decimal places.



Answer 1

If you should use Z-table (like this one: https://www.z-table.com) you should find z-value for the given area.

1. z-value that corresponds to the lower 18.22 % of the data: the area to the left under the Z-curve should be 0.1822.

From Z-table we can find:

z = -0.90 Area to the left is 0.1841

z = -0.91 Area to the left is 0.1814 (closer to 0.1822)

Round to 2 decimal places: z-value = -0.91

1. z-value that corresponds to the upper 6.85 % of the data: the area to the right under the Z-curve should be 0.0685. So the area to the left is 1 - 0.0685 = 0.9315

From Z-table we can find:

z = 1.48 Area to the left is 0.9306

z = 1.49 Area to the left is 0.9319 (closer to 0.9315)

Round to 2 decimal places: z-value = 1.49

But if you can use TI-83, TI-84, or TI-36, you can find these values more accurate with no using Z-table.

For TI-83:

invNorm(0.1822,0,1) = -0.9070 ≈ -0.91

invNorm(0.9315,0,1) = 1.4870... ≈ 1.49