7.82 In order to test the durability of a new paint, a high- way department had test strips painted across heavily traveled roads in 15 different locations. If on the av- erage the test strips disappeared after they had been crossed by 146,692 cars with standard deviation of 14,380 cars, construct a 99% confidence interval for the true average number of cars it takes to wear off the paint. Assume a normal population.
7.83 Referring to Exercise 7.82 and using 14,380 as an es- timate of $\sigma$, find the sample size that would have been needed to be able to assert with 95% confidence that the sample mean is off by at most 10,000. [Hint: First estimate $n_1$ by using $z = 1.96$, then use $t_{0.025}$ for $n_1 - 1$ degrees of freedom to obtain a second estimate $n_2$, and repeat this procedure until the last two values of $n$ thus obtained are equal.]
