bannaconde79Lv1

29 Jan 2023

Introduction to Statistics

Task 6: Using the Z table to Link Raw Scores, Z scores, and Proportions or Percents

The entire normal distribution is 1.00(100%) and each Z value defines a point in the normal distribution where a certain proportion lies below the Z value and another proportion lies above it. Sometimes you have a Z value and want to know the proportion above or below. Sometimes you have a particular proportion in mind and you need to know what Z value, or raw score defines that proportion. For this we use a Unit Normal Table (aka Z table.)

Complete the table. A few Z values have been provided. Look up the others by first locating the described proportion in the Z table, then finding the Z value that goes with that proportion. For these assignments use only the table provided in the GWFW textbook or the one posted in Discussions. Do not use any other source or your answers may be marked wrong.

 

Reminder:     Proportion * 100=

Percent         (Percent/100) = Proportion

 

There are two Options for converting a Z value to a value in a distribution with a know mean and standard deviation. Use whichever you prefer.

Basic Formula:      Score = + ()      !! You must make sure you have the correct sign for Z!!

Alternate:    You can use the absolute value of Z from the table, and modify the formula to either add to the mean or subtract from it. Visualizers may prefer this method.

For locations below the mean use: Score = - ()

For locations above the mean use: Score = + ()

Check that your answers make sense. (e.g., lower tail values should be lower than the mean.)

 

Use the same mean and standard deviation values reported in Tasks 1 and 2 .

Round answers to 2 decimals.

 

Location: 'The point where...'	Z	HR	RR
Exactly 33% is in the lower tail
At least 0.10 is in the in the upper tail
No more than 5% is in the upper tail	1.65
Exactly 0.025 is in the lower tail	-1.96
Exactly 2.5% is in the upper tail
No more than 1% is in the lower tail
No more than 0.005 is the upper tail	2.58