z = (75 - 85)/5 = -10/5 = -2
Mean 0, standard deviation 1.
The mean of a distribution gives no information about the standard deviation.
It is the value that is one standard deviation greater than the mean of a Normal (Gaussian) distribution.
Standard deviation describes the spread of a distribution around its mean.
z=(x-mean)/(standard deviation of population distribution/square root of sample size) T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute. t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)
The mean is 46.
No. The standard deviation is not exactly a value but rather how far a score deviates from the mean.
It is the normalised Gaussian distribution. To speak of a 'standard z' distribution is somewhat redundant because a z-score is already standardised. A z-score follows a normal or Gaussian distribution with a mean of zero and a standard deviation of one. It's these specific parameters (this mean and standard deviation) that are considered 'standard'. Speaking of a z-score implies a standard normal distribution. This is important because the shape of the normal distribution remains the same no matter what the mean or standard deviation are. As a consequence, tables of probabilities and other kinds of data can be calculated for the standard normal and then used for other variations of the distribution.
Mean 0, standard deviation 1.
The mean of a distribution gives no information about the standard deviation.
It is the value that is one standard deviation greater than the mean of a Normal (Gaussian) distribution.
Standard deviation describes the spread of a distribution around its mean.
IQ is distributed normally, with a mean of 100 and a standard deviation of 15. The z-score of 100 is therefore:(value-mean)*standard deviation= (100-100)*15= 0More generally, a raw score that is equivalent to the mean of a normal distribution will always have a z-score of 0.
z=(x-mean)/(standard deviation of population distribution/square root of sample size) T-score is for when you don't have pop. standard deviation and must use sample s.d. as a substitute. t=(x-mean)/(standard deviation of sampling distribution/square root of sample size)
It depends on what the distribution is. In a Normal or Gaussian distribution, the standard deviation is the square root of the mean, so it could be 3.1 but, again, it depends on the distribution.
score of 92
The standard normal distribution has a mean of 0 and a standard deviation of 1.