A positive value of z indicates the sample mean is more than the population mean.
What is normal distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
The z-score or the standardized normal distribution score is defined as:
z = (x - µ)/(√σ/n)
Here,
x = sample mean
µ = population mean
σ = population standard deviation
n = 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 z is positive or negative is determined by the value of x and µ.
If z = positive, this implies that
x - µ > 0
x > µ
That is the sample mean is greater than the population mean.
If z = negative, this implies that
x - µ < 0
x < µ
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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