Question

4.17 During the assembly of an exhaust valve, sufficient dis- tance 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.

Answer 1

here this is binomial distribution with paramter p=0.85 and n=20

a)P( at least 15 will have required distance ) =P(X>=15) = $\small \sum_{x=15}^{20}\binom{20}{x}(0.85)^{x}(0.15)^{20-x}$ =0.9327

b)P(at most 10 will have required distance ) =P(X<=10) = $\small \sum_{x=0}^{10}\binom{20}{x}(0.85)^{x}(0.15)^{20-x}$ =0.0002

c)

P(exactly 18 will have required distance)=P(X=18)= $\small \binom{20}{18}(0.85)^{18}(0.15)^{2}$ =0.2293