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Why Normal distribution is better then other distributions in statistics?
The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.
What information must you know in order to completely specify the shape of a normal distribution?
the mean and the standard deviation
How do you find the interquartile range when given the mean and standard deviation?
In general you cannot. You will need to know more about the distribution of the variable - you cannot assume that the distribution is uniform or Normal.
If normal distribution is between 110 and 190 how can I find the probability that it will be between 135 and 165?
You need to know the standard deviation or standard error to answer the question.
What are 5 questions you could ask a student about probability distribution?
The answer depends on the level at which the student is expected to be. A 15-year old should know the probability of getting heads on the toss of a coin but even a mathematics graduate - who did not specialise in probability - would be expected to be able to prove the mathematical relationship between the Normal distribution and the F-distribution. If asked, most student would not even know what the second part of the sentence meant.
