(A) The perfect standard normal distribution (or simply the standard normal
distribution) is the normal distribution with a mean of zero (m = 0) and a variance of
one (s^2 = 1). As such it shares all the characteristics of a normal distribution such
(i) The distribution is bell shaped
(ii) The normal probability density function is symmetric about its mean value
(iii) The mean, median and mode of the distribution coincide (all are 0)
(iv) The inflection points of the curve occur at one standard deviation away from the
(B) Yes, one can have two normal distributions with the same mean and different
standard deviations. For example, two groups of students may have scored the
same average score on a Math test, but if the students of one group were a mix of
good and poor abilities, and the other group consisted of students who were
consistently good at Math, then the two groups would have different standard
deviations (the first group would have higher standard deviation than the second).
Their scores when plotted would still have a symmetric bell shape (normal
(C) It is very easy to identify a normal distribution from its graph. It has a peak
(corresponding to the mean value), and has a bell shape. The curve is a mirror
image on both sides of the peak, and tapers off on either side.
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