Some important properties of are listed below:
(i) has mean, median and mode all equal to zero.
(ii) The standard deviation of is 1. Also the approximate values of mean deviation and quartile deviation are 0.8 and 0.675 respectively.
(iii) The standard normal distribution is symmetrical about = 0.
(iv) The two points of inflexion of the probability curve of the standard normal distribution are –1 and 1.
(v) The two tails of the standard normal curve never touch the horizontal axis.
(vi) The upper and lower p per cent points of the standard normal variable z are given by
(since for a standard normal distribution
Selecting P = 0.005, 0.025, 0.01 and 0.05 respectively,
These are shown in fig 17.3.
(vii) If denotes the arithmetic mean of a random sample of size n drawn from a normal population then,