(a) What is the shape of the probability distribution obtained by plotting rando
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Question
(a) What is the shape of the probability distribution obtained by plotting random numbers in a frequency diagram? (b) What kind of distribution is obtained by sampling from this distribution (assuming the sample size is sufficiently large)? (b) What is the name of the theorem that proves this important result? (d) What is the recommended ('sufficiently large') minimum sample size to be used when the distribution of the population being investigated is either unknown or known not to be Normal? (e) What is the relationship between the standard deviation, sigma, of a population and the standard deviation, s, of a sample of size n drawn from that population? (In words or in the form of an algebraic expression.)Explanation / Answer
a. A histogram is a graphical representation of the distribution of numerical data. It is an estimate of theprobability distribution of a continuous variable .
The central limit theorem in it's shortest form states that the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger, regardless of the shape of the population distribution.
b. Normal
c. Central limit theorem
d. n>=30
The central limit theorem states that: Given a population with a finite mean and a finite non-zero variance 2, the sampling distribution of the mean approaches a normal distribution with a mean of and a variance of 2/N as N, the sample size, increases.
e. s=/N
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