When an audit must be conducted that involves a tedious examination of a large

inventory, the audit may be very costly and time consuming if each item in the inventory must

be examined. In such situations, the auditor frequently obtains a random sample of items from

the complete inventory and uses the results of an audit of the sampled items to check the validity

of the company's financial statement. A large company$$s financial statement claims an inventory

that averages $$600$ per item. The following data are the auditor$$s assessment of a random sample

of $75$ items from the company$$s inventory. The values resulting from the audit are rounded to

the nearest dollar.

$3035471,3684939845071482,546738832135274741,472$

$3991,784717511365711472822,0391,9097481885481280$

$1026181291,3241,4284691024541,05993930360023451417$

$5512931,39572829735065118121,2906854471135$

$2521,52646456799672597672483,21533341$

a$.$ Estimate the mean value of an item in the inventory using a $95\%$ confidence

interval.

b$.$ Is there substantial evidence $($a $\mathrm{.}01)$ that the mean value of an item in the

inventory is less than $$600?$

c$.$ What is the target population for the above inferences?

d$.$ Would normal dist