Use Table 4-1 for this exercise. Suppose that the mileage at which 10000 sets of automobile brakes had been 80% worn through was recorded. The average was 62700, and the standard deviation was 10 400 miles.

(a) What fraction of brakes is expected to be 80% worn in less than 40 860 miles?

(b) What fraction is expected to be 80% worn at a mileage between 57500 and 71020 miles?

Table 4-1

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Area |2 1.4 y Area y Area 0.0 0.398 9 0.000 0 0.149 7 0.419 2 2.8 0.007 9 0.497 4 0.1 0.397 0 0.039 8 1.5 0.129 5 0.433 2 2.9 0.006 0 0.498 1 0.2 0.391 0 0.079 3 1.6 0.110 9 0.445 2 3.0 0.004 4 0.498 650 0.3 0.381 4 0.117 9 1.7 0.094 1 0.455 4 3.1 0.003 3 0.499 032 0.4 0.368 3 0.155 4 1.8 0.079 0 0.464 1 3.2 0.002 4 0.499 313 0.5 0.352 1 0.191 5 1.9 0.065 6 0.471 3 3.3 0.001 7 0.499 517 0.6 0.333 2 0.225 8 2.0 0.054 0 0.477 3 3.4 0.001 2 0.499 663 0.7 0.312 3 0.258 0 2.1 0.044 0 0.482 1 3.5 0.000 9 0.499 767 0.8 0.289 7 0.288 1 2.2 0.035 5 0.486 1 3.6 0.000 6 0.499 841 0.9 0.266 1 0.315 9 2.3 0.028 3 0.489 3 3.7 0.000 4 0.499 904 1.0 0.242 0 0.341 3 2.4 0.022 4 0.491 8 3.8 0.000 3 0.499 928 1.1 0.217 9 0.364 3 2.5 0.017 5 0.493 8 3.9 0.000 2 0.499 952 1.2 0.194 2 0.384 9 2.6 0.013 6 0.495 3 4.0 0.000 1 0.499 968 1.3 0.171 4 0.403 2 2.7 0.010 4 0.496 5 0.5