Question
Asked Mar 5, 2019
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Use a table of cumulative areas under the normal curve to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find thez-score.
 
0.051
The cumulative area corresponds to the z-score of  
(Round to three decimal places as needed.)
 
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Expert Answer

Step 1

Z-score:

The Z-score measures a particular value’s relationship to the mean in a group of values. It gives the number of standard deviation from the mean for the particular data point.

The general formula to obtain Z-score is,

Z = (x – population mean) / population standard deviation.

Standardized variables:

Standardized variables are the variables which are rescaled using the Z-score and these variables will have mean 0 and standard deviation 1.

Step 2

Here, z = 0.051.

The standard normal cumulative function (CDF) is usually denoted by Φ(z) = P(Z < z).

The CDF corresponding to the value 0.051 is not in the table. Therefore, consider the value 0.05 which is close to 0.051.The value 0.05 of the standard normal variable can be found from the standard normal table of cumulative probabilities, by using the following procedure:

  • Locate the value 0 in the first column, named Z.
  • Move towards the right along the row of 0.0, till the 6th column, named 05 is reac...

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