What sample size is necessary for a study

Problem is:

What sample size is ncessary for a study to determine the average cost of a child delivered at a local hopsital within the past 3 months? (I have determined a sample size of 1,300. I came up with this number because there are 10,416 births a year in Louisville, KY where the basis of this problem is. 10,416 / 12 months = 868. 868 x 3 months = 2,604 so I am taking half of that and rounding to 1,300.

The remainder of the question is: The mean sample is estimated to be $10,000 with a population standard deviation of $1,500 and the research objectives are a 95% confidence interval and the error range is $500.

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