During the assembly of an exhaust valve, sufficient distance must be maintained between the valve tip and the cylinder wall. If \(85 \%\) of valve assemblies have the required distance, use Table 1 or software to find the probabilities that among 20 such valves:

(a) at least 15 will have the required distance;

(b) at most 10 will have the required distance;

(c) exactly 18 will have the required distance.

Data From Table 1

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Table 11.1 Time to assess problem when a relay tower breaks down Difficulty Assessment Level Difficulty Experience(yr) Time Simple 0 1.5 3.0 Simple 0 2.0 2.3 Simple 0 4.5 1.7 Simple 0 8.0 1.2 Complex 1 1.5 6.7 Complex 1 0.5 7.1 Complex 1 2.5 5.3 Complex 1 3.0 5.0 Complex 1 5.0 5.6 Complex 1 6.0 4.5 Simple 0.0 4.5 Simple 0 0.5 4.7 Simple 0 3.5 4.0 Simple 0 4.0 4.5 Simple 0 5.0 3.1 Simple 0 6.0 3.0 Complex 1 0.0 7.9 Complex 1 3.0 6.9 Complex 1 5.5 5.0 Complex 1 5.0 5.3 Complex 1 3.5 6.9