SOLUTION: 5. The following questions pertain to some important facts to know about a normal distribution: a. What are three important properties of a normal distribution? b. What percenta

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Question 1200097: 5. The following questions pertain to some important facts to know about a normal
distribution:
a. What are three important properties of a normal distribution?
b. What percentage of the values are:
i. Within 1 standard deviation of the mean?
ii. Two standard deviations or more above the mean?

Answer by amarjeeth123(569) (Show Source):
You can put this solution on YOUR website!
Properties of normal distribution
1) The normal curve is bell shaped in appearance.
2) There is one maximum point of normal curve which occur at mean.

3) As it has only one maximum curve so it is unimodal.
4) In binomial and possion distribution the variable is discrete while in this it is continuous.
5) Here mean= median =mode.
6) The total area of normal curve is 1. The area to the left and the area to the right of the curve is 0.5.
7) No portion of curve lies below x-axis so probability can never be negative.
8) The curve becomes parallel to x-axis which is supposed to meet it at infinity.
9) Here mean deviation = 4/5 standard deviation.
10) Quartile deviation = 5/6 mean deviation
11) Quartile deviation : mean deviation : standard deviation
10 : 12 : 15

12) 4 standard deviation = 5 mean deviation = 6 quartile deviation
68% of the data is less than 1 standard deviation away from the mean (1SD). 95% of the data is less than two standard deviations away from the mean. 99.7% of the data is less than three.