Question

Express the given z into a three - digit form
z=.56

Answer 1

Answer:

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Answer 2

Answer:

Given any data value, we can identify how far that data value is away from the mean, simply by doing a subtraction x – μ. This value will be positive if your data value lies above (to the right) of the mean, and negative if it lies below (to the left) of the mean. But what we’d really like to know is, relative to the spread of our data set, how far is x from μ? Remember that the standard deviation σ gives us a measure of how spread out our entire set of individual data values is.

The z-score for any single data value can be found by the formula (in English):

Equation

or with symbols (as seen before!):

Equation

Obviously a z-score will be positive if the data value lies above (to the right) of the mean, and negative if the data value lies below (to the left) of the mean.

Example 6.1: Calculating and Graphing z-Values

Given a normal distribution with μ = 48 and s = 5, convert an x-value of 45 to a z-value and indicate where this z-value would be on the standard normal distribution.

Solution

Begin by finding the z-score for x = 45 as follows.

Sec03. z-score