If \(95 \%\) of certain high-performance radial tires last at least 30,000 miles, find the mean and the standard deviation of the distribution of the number of these tires, among 20 selected at random, that last at least 30,000 miles, using

(a) Table 1, the formula which defines \(\mu\), and the computing formula for \(\sigma^{2}\).

(b) the special formulas for the mean and the variance of a binomial distribution.

Data From Table 1

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Table 1.1 Slot depth (thousandths of an inch) Time 6:30 7:00 7:30 8:00 8:30 9:00 9:30 10:00 1 214 218 218 216 217 218 218 219 2 211 217 218 218 220 219 217 219 3 218 219 217 219 221 216 217 218 Sum 643 654 653 653 658 653 652 656 214.3 218.0 217.7 217.7 219.3 217.7 217.3 218.7 Time 10:30 11:00 11:30 12:30 1:00 1:30 2:00 2:30 1 216 216 218 219 217 219 217 215 2 219 218 219 220 220 219 220 215 3 218 217 220 221 216 220 218 214 Sum 653 651 657 660 653 658 655 644 217.7 217.0 219.0 220.0 217.7 219.3 218.3 214.7