A survey conducted in Honeytown found that the average number of people per household was $4.3$ with a standard deviation of $1.2$. The true average size and standard deviation of a household in Honeytown is $4.1$ and $0.98$ respectively.

Using simple random samples of size $50$, what are the mean and standard deviation for the sampling distribution of the sample means of the number of people per household in Honeytown?

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