Discussion
Sampling distribution of mean is very close to the standard normal distribution when
Answer: C
The sampling distribution of the mean is very close to the standard normal distribution in both cases: when the population is itself normal, and when it is not normal but the sample size is large. The first holds exactly; the second follows from the central limit theorem, which says that the distribution of the sample mean approaches normality as the sample size grows.
Therefore the combined option 'Both (A) and (B)' is correct, and the options that accept only one of the two or neither are incomplete or wrong. The standard normal form is reached by standardising the mean with its mean and standard error.
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