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steposvetlana [31]
3 years ago
10

For a normal distribution, a positive value of z indicates that _______.

Mathematics
1 answer:
klasskru [66]3 years ago
3 0

Answer:

A positive value of <em>z</em> indicates the sample mean is more than the population mean.

Step-by-step explanation:

The <em>z</em>-score or the standardized normal distribution score is defined as:

                                            z=\frac{\bar x-\mu}{{\frac{\sqrt{\sigma} }{n} } }

Here,

\bar x = sample mean

\mu = population mean

\sigma = population standard deviation

<em>n</em> = sample size.

The value of population standard deviation is always positive since it is the square of the deviations of values from their mean.

Then if the value of <em>z</em> is positive or negative is determined by the value of \bar x and \mu.

  • If <em>z</em> = positive, this implies that

          \bar x-\mu>0\\\bar x>\mu

       That is the sample mean is greater than the population mean.

  • If <em>z</em> = negative, this implies that

          \bar x-\mu

       That is the sample mean is smaller than the population mean.

Thus, a positive value of z indicates the sample mean is more than the population mean.

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