Determine the value z that satisfies the conditions below Ro

Determine the value z* that satisfies the conditions below. (Round all answers to two decimal places.) Can you please show all the steps

(a) Separates the largest 3.3% of all z values from the others
z* =

(b) Separates the largest 1% of all z values from the others
z* =

(c) Separates the smallest 5.6% of all z values from the others
z* =

(d) Separates the smallest 16.6% of all z values from the others
z* =

You may need to use the appropriate table in Appendix A to answer this question.

Solution

(a) Separates the largest 3.3% of all z values from the others

The percentage of all z values below z* woule be 100%-3.3%=96.7%

Now look into standard normal table for area closest to 0.9670, which is 0.9671 (because standard normal table uses area left to z score) and corresponding z score is 1.84. Therefore:
z* = 1.84

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(b) Separates the largest 1% of all z values from the others

The percentage of all z values below z* woule be 100%-1%=99%

Now look into standard normal table for area closest to 0.9900, which is 0.9901 (because standard normal table uses area left to z score) and corresponding z score is 2.33. Therefore:
z* = 2.33

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(c) Separates the smallest 5.6% of all z values from the others

Look into standard normal table for area closest to 0.0560, which is 0.0559 (because standard normal table uses area left to z score) and corresponding z score is -1.59. Therefore:
z* = -1.59

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(d) Separates the smallest 16.6% of all z values from the others

Look into standard normal table for area closest to 0.1660, which is 0.1660 (because standard normal table uses area left to z score) and corresponding z score is -0.97. Therefore:
z* = -0.97