A clothing store has an inventory of 920 different items. In order to estimate the total dollar value of inventories, an auditor takes a simple random sample of the items. On the basis of last year’s data, the population standard deviation is estimated to be $97. The auditor would like to produce, for the population total, a 95 % confidence interval that extends $16.30 on each side of the sample estimate. How large a sample size is necessary to meet this requirement?