Question

please help me explain these question statement!

(Based on Normal Distribution, Sampling Distribution part)

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Answer 1

1) Since the sample mean is a linear combination of the sample data points, hence it also follows normal distribution. Now observe that

where μ population mean and o-- population variance

Hence $\\ \overline{X} \sim N(\mu , \sigma^2/n)$ . From this information we can calculate the probability of sample mean when population mean and population variance is given.