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Chirag, Master's Degree
Category: Calculus and Above
Satisfied Customers: 12192
Experience:  I have a Master's degree in Engineering and a very wide teaching experience of more than 25 years at various levels.
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# What are the characteristics of a standard normal distribution?

### Resolved Question:

What are the characteristics of a standard normal distribution? Can two distributions with the same mean and different standard distributions be considered normal? How might you determine if a distribution is normal from its graphical representation?
Submitted: 5 years ago.
Category: Calculus and Above
Expert:  Chirag replied 5 years ago.
Hi, Welcome to Just Answer and Thanks for this request.

I am working on this and will post the answer as soon as finished.

Thanks.
Expert:  Chirag replied 5 years ago.

(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

as

(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

mean

(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

distribution)

(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.

Kindly ACCEPT my answer so that I get the Credit. BONUS is welcome.

Thanks.

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