1 point
Let X is random variable with mean 'm' and variance '2! The standardised form of
Xis Z = What are the mean and variance respectively of Z?
X-m
O (2,0)
O (2,1)
0 (0,1)
O (1,0)
W
Answers
The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. The calculation is as follows:
x = μ + (z)(σ) = 5 + (3)(2) = 11
The z-score is three.
The mean for the standard normal distribution is zero, and the standard deviation is one. The transformation
z
=
x
−
μ
σ
produces the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.
The following two videos give a description of what it means to have a data set that is “normally” distributed.
Z-Scores
If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is:
z
=
x
−
μ
σ
The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z-scores, and values of x that are smaller than the mean have negative z-scores. If x equals the mean, then x has a z-score of zero.