[Solution] Identify the distribution of the sample mean. In particular, state whether the distribution of x̄ is normal or approximately normal and give


Question: Identify the distribution of the sample mean. In particular, state whether the distribution of \(\bar{x}\) is normal or approximately normal and give its mean and standard deviation.

For the population of one town, the number of siblings, \(x\), is a random variable whose

relative frequency histogram has a reverse J-shape. The mean number of siblings is 1.2 and the standard deviation is 1.5. Let \(\bar{x}\) denote the mean number of siblings for a random sample of size 35. Determine the sampling distribution of the mean for samples of size 35.

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