Bloomingdale's main store in New York has the following departments on its mezzanine level: Stendahl, Ralph Lauren, Beauty Spot, and Lauder Prescriptive. The mezzanine level is managed separately from the other levels, and during the store's post holiday sale, the level manager wanted to estimate the average sales amount per customer throughout the sale. The following table gives the relative weights of the different departments (known from previous operation of the store), as well as the sample means and variances of the different strata for a total sample of 1,000 customers, proportionally allocated to the four strata. Give a 95% confidence interval for the average sale (in dollars) per customer for the entire level over the period of the post holiday sale.
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