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0.3829 approx.
The binomial distribution can be approximated with a normal distribution when np > 5 and np(1-p) > 5 where p is the proportion (probability) of success of an event and n is the total number of independent trials.
77.45%
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
Assuming a normal distribution, the proportion falling between the mean (of 8) and 7 with standard deviation 2 is: z = (7 - 8) / 2 = -0.5 → 0.1915 (from normal distribution tables) → less than 7 is 0.5 - 0.1915 = 0.3085 = 0.3085 x 100 % = 30.85 % (Note: the 0.5 in the second sum is because half (0.5) of a normal distribution is less than the mean, not because 7 is half a standard deviation away from the mean, and the tables give the proportion of the normal distribution between the mean and the number of standard deviations from the mean.)
It is 0.158655, approx.
0.0668 or about 1/15
There is no specific proportion: the answer depends on the level of significance beyond which subjects are considered to be outliers.
0.15542174161
0.419243340766
It is 0.158655 or 0.159 approx.is the anwer 0.8413, -0.3413, -0.1587, 0.1587
0.866
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11.51% of the distribution.
2.27%
2.27
Prob(-0.5 < z < 0.5) = 0.3830