A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is required to break the insulators. You measure force by observing how many pounds are applied to the insulator before it breaks. The accompanying data represent the amount of force required to break a sample of 30 insulators. Complete parts (a) through (c) below.

1870,1728,1656,1610,1634,1784,1522, 1696,1592,1662,1866,1764,1734,1662, 1734,1774,1550,1756,1762,1866,1820, 1744,1788,1688,1810,1752,1680,1810, 1652,1736

a. construct a 95% confidence interval estimate for the population mean force.

b. what assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?

c. do you think the assumption needed in order to construct the confidence interval estimate in (a) is valid? explain.