Question

A standardized variable always has a mean of​ _______ and a standard deviation of​ _______. b. The​ z-score corresponding to an observed value of a variable tells you​ _______. c. A positive​ z-score indicates that the observation is​ ______ the​ mean, whereas a negative​ z-score indicates that the observation is​ _______ the mean

Answer 1

Explanation:

We know that normal distribution as special characteristics such as symmetry, unimodal, no skewness, mean =median=mode, etc

A standardized variable for normal variable X is

`Z = (x-\mu)/(\sigma)` will be normal with mean =0 and sigma =1

The probability will be divided equally on either side of the mean =0 i.e. y axis

Hence the answers would be

A standardized variable always has a mean of​ __0_____ and a standard deviation of​ ___1____. b. The​ z-score corresponding to an observed value of a variable tells you​ ____the std normal score.___. c. A positive​ z-score indicates that the observation is​ __to the right ____ the​ mean, whereas a negative​ z-score indicates that the observation is​ __to the left_____ the mean